Sign up
Math

Linear Algebra

Get personalized support from expert tutors and AI-powered study tools.

Personalized practice Exam · Set a test date 8 units · 77 topics
Generate study planExplore skills
Your study plan
Free with a Varsity Tutors account
Free
Turn this Linear Algebra outline into a plan
A week-by-week plan
Paced to your test date and rebuilt whenever your Linear Algebra scores move.
A score projection
See where you stand today and what each study block is worth.
Progress that sticks
Lessons, flashcards, and quizzes tracked in one place, on every device.
Create your free plan
Takes a minute · No credit card required
Your next tutoring session · Linear Algebra prep Ready when you are
No upcoming Linear Algebra tutoring session scheduled
Book a tutoring session when you are ready to work with an expert.
Book a tutor

Ways to study

Subject resources
Long-form
Long-form Lessons
Open lessons
1,355 questions
Quizzes
Take a quiz
1 test
Full-length Practice Tests
Start a test

Linear Algebra

Practice 77 skills across this outline.

Recommended next
Similarity & Change of Basis
Eigenvalues & Eigenvectors · Diagonalization and Similarity
Long-form lesson
Weighting distribution
19 categories
Problem-Solving & Modeling Tools · Computation Workflow and Interpretation
8%
Determinants · Determinants and Invertibility
7%
Linear Transformations · Transformations and Matrices
7%
Determinants · Determinant Computation
6%
Matrix Decompositions & Structure · Diagonalization Variants
6%
Matrix Decompositions & Structure · Rank, Nullity, and Fundamental Spaces
6%

Skills

The comprehensive taxonomy of linear algebra — drill into a card to work its skills.

Eigenvalues & Eigenvectors · Diagonalization and Similarity

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Similarity & Change of BasisRecommended
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Complex Eigenvalues & Real SolutionsAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Matrix Powers via DiagonalizationAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
DiagonalizationAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Eigenvalues & Eigenvectors · Applications of Eigenvalues

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Stability in Linear SystemsAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Markov Chains & Steady StatesAvailable
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Principal Directions & Quadratic FormsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Eigenvalues & Eigenvectors · Eigenvalues and Eigenvectors

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Characteristic PolynomialAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Algebraic vs. Geometric MultiplicityAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Eigenvectors & EigenspacesAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Eigenvalues: Special MatricesAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Problem-Solving & Modeling Tools · Computation Workflow and Interpretation

4 core skills8% total weight
0/4 completed
4 skills to mastery
1
Common Errors & PitfallsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Choosing Solution MethodsAvailable
22 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Parametric SolutionsAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Verifying Solutions & IdentitiesAvailable
10 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Problem-Solving & Modeling Tools · Applications and Modeling

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Modeling with Linear SystemsAvailable
7 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Linear Algebra in DEsAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Geometric ApplicationsAvailable
13 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Systems of Linear Equations & Matrices · Inverses and Solving Ax=b

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Solving Ax=b via InversesAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Invertible MatricesAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
LU DecompositionAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Computing Matrix InversesAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Systems of Linear Equations & Matrices · Systems of Linear Equations

5 core skills4% total weight
0/5 completed
5 skills to mastery
1
Parametric Solutions & Free VariablesAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Setting Up Linear SystemsAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Gaussian EliminationAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Consistent vs. Inconsistent SystemsAvailable
17 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
5
RREF & Solution InterpretationAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Systems of Linear Equations & Matrices · Matrix Operations

5 core skills4% total weight
0/5 completed
5 skills to mastery
1
Transpose & Symmetric MatricesAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Matrix-Vector ProductsAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Elementary MatricesAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Identity MatricesAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
5
Matrix OperationsAvailable
13 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Determinants · Determinant Computation

4 core skills6% total weight
0/4 completed
4 skills to mastery
1
Determinants via Row ReductionAvailable
16 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
2x2 & 3x3 DeterminantsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Determinant PropertiesAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Cofactor Expansion & MinorsAvailable
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Determinants · Determinants and Invertibility

4 core skills7% total weight
0/4 completed
4 skills to mastery
1
Area/Volume ScalingAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Determinant & InvertibilityAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Cramer's RuleAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Determinant Orientation & SignAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Inner Product Spaces & Orthogonality · Orthogonal Bases and QR

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
QR FactorizationAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Orthonormal BasesAvailable
13 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Gram-Schmidt ProcessAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Orthogonal MatricesAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Inner Product Spaces & Orthogonality · Dot Product and Norms

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Projections & DecompositionsAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Dot Product & AnglesAvailable
13 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Orthogonality & ComplementsAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Vector Norms & DistanceAvailable
16 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Inner Product Spaces & Orthogonality · Least Squares and Applications

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Normal EquationsAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Linear Regression via Least SquaresAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Best ApproximationAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Least Squares SolutionsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Linear Transformations · Geometry of Transformations

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Geometric Matrix TransformationsAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Projections onto Lines & SubspacesAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Transformations in R^2 & R^3Available
19 questions 0 flashcards Lesson available
Long-form lessonFlashcards — not available yetPractice problems
4
Scaling & StretchingAvailable
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Linear Transformations · Transformations and Matrices

5 core skills7% total weight
0/5 completed
5 skills to mastery
1
Composition of TransformationsAvailable
17 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Linear Transformation DefinitionAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
One-to-One & OntoAvailable
22 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Matrix RepresentationAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
5
Kernel & RangeAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Matrix Decompositions & Structure · Diagonalization Variants

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Orthogonal DiagonalizationAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Spectral TheoremAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Singular Value Decomposition (SVD)Available
8 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Matrix Decompositions & Structure · Rank, Nullity, and Fundamental Spaces

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Row, Column, and SpaceAvailable
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Rank-Nullity TheoremAvailable
16 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Rank & NullityAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Vector Spaces & Subspaces · Linear Independence and Basis

5 core skills6% total weight
0/5 completed
5 skills to mastery
1
Basis & DimensionAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Linear IndependenceAvailable
17 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Finding a BasisAvailable
16 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Coordinate VectorsAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
5
Change of BasisAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Vector Spaces & Subspaces · Vector Space Fundamentals

5 core skills6% total weight
0/5 completed
5 skills to mastery
1
Span & Generating SetsAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Subspaces & TestsAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Vectors in R^nAvailable
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Vector Space DefinitionAvailable
22 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
5
Column Space & Null SpaceAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Live Classes

Scheduled, expert-led Linear Algebra classes you attend live.
Browse all
SAT Math 1-Week Bootcamp
LIVE
Test Prep
SAT Math

SAT Math 1-Week Bootcamp

Aug 17, 2026·12:00 AM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
SAT Math Cram Session
LIVE
Test Prep
SAT Math

SAT Math Cram Session

Aug 18, 2026·10:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
One-time class
Summer Learning: Bridging the Gap to 5th Grade Math
LIVE
Math
Elementary School Math

Summer Learning: Bridging the Gap to 5th Grade Math

Aug 18, 2026·11:30 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 6th Grade Math
LIVE
Math
Middle School Math

Summer Learning: Bridging the Gap to 6th Grade Math

Aug 19, 2026·12:00 AM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 7th Grade Math
LIVE
Math
Middle School Math

Summer Learning: Bridging the Gap to 7th Grade Math

Aug 19, 2026·10:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 4th Grade Math
LIVE
Math
Elementary School Math

Summer Learning: Bridging the Gap to 4th Grade Math

Aug 19, 2026·11:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 8th Grade Math
LIVE
Math
Middle School Math

Summer Learning: Bridging the Gap to 8th Grade Math

Aug 19, 2026·11:30 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 1st Grade Math
LIVE
Math
Elementary School Math

Summer Learning: Bridging the Gap to 1st Grade Math

Aug 25, 2026·10:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class

Related Linear Algebra tutors

Browse tutors who can help with this subject.
View all tutors
Expert tutoring

No related Linear Algebra tutors found

Browse the full gallery to find a vetted expert who can help with Linear Algebra.