MIT · 18.06

Linear Algebra

线性代数

Matrices, vector spaces, eigenvalues, and linear transformations.

Subject：Linear Algebra

Level：Undergraduate

Suggested stage：Years 2–3 (inferred)

Public-material edition：2010

Language：English

Videos：Available

Assignments / solutions：Available / Available

Prerequisites

Multivariable Calculus →

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▶Lectures, video & readingCourse content in the official sequence32

The geometry of linear equations Elimination with matrices Multiplication and inverse matrices Factorization into A = LU Transposes, permutations, and vector spaces Column space and nullspace Solving Ax = 0 Solving Ax = b Independence, basis, and dimension The four fundamental subspaces Matrix spaces and rank one Graphs, networks, and incidence matrices Orthogonal vectors and subspaces Projections onto subspaces Projection matrices and least squares Orthogonal matrices and Gram-Schmidt Properties of determinants Determinant formulas and cofactors Cramer's rule, inverse matrix, and volume Eigenvalues and eigenvectors Diagonalization and powers of A Differential equations and exp(At)Markov matrices and Fourier series Symmetric matrices and positive definiteness Complex matrices and FFT Positive definite matrices and minima Similar matrices and Jordan form Singular value decomposition Linear transformations and their matrices Change of basis and image compression Left and right inverses; pseudoinverse Final course review

✓Assignments & practiceOpen the matching problem or assignment page31

Problems: The geometry of linear equations Problems: Elimination with matrices Problems: Multiplication and inverse matrices Problems: Factorization into A = LU Problems: Transposes, permutations, and vector spaces Problems: Column space and nullspace Problems: Solving Ax = 0 Problems: Solving Ax = b Problems: Independence, basis, and dimension Problems: The four fundamental subspaces Problems: Matrix spaces and rank one Problems: Graphs, networks, and incidence matrices Problems: Orthogonal vectors and subspaces Problems: Projections onto subspaces Problems: Projection matrices and least squares Problems: Orthogonal matrices and Gram-Schmidt Problems: Properties of determinants Problems: Determinant formulas and cofactors Problems: Cramer's rule, inverse matrix, and volume Problems: Eigenvalues and eigenvectors Problems: Diagonalization and powers of A Problems: Differential equations and exp(At)Problems: Markov matrices and Fourier series Problems: Symmetric matrices and positive definiteness Problems: Complex matrices and FFT Problems: Positive definite matrices and minima Problems: Similar matrices and Jordan form Problems: Singular value decomposition Problems: Linear transformations and their matrices Problems: Change of basis and image compression Problems: Left and right inverses; pseudoinverse

◇Exams & quizzesOfficial quizzes, exams and review material4

Exam 1 Exam 2 Exam 3 Final exam

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