18.06
Linear Algebra
Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, singular value decomposition, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses linear algebra software. Compared with 18.700 , more emphasis on matrix algorithms and many applications.
Spring 2010
Topics
- The geometry of linear equations
- Elimination with matrices
- Matrix operations and inverses
- LU and LDU factorization
- Transposes and permutations
- Vector spaces and subspaces
- The nullspace: Solving Ax = 0
- Rectangular PA = LU and Ax = b
- Row reduced echelon form
- Basis and dimension
- The four fundamental subspaces
- Graphs and networks
- Orthogonality
- Projections and subspaces
- Least squares approximations
- Gram-Schmidt and A = QR
- Properties of determinants
- Formulas for determinants
- Applications of determinants
- Eigenvalues and eigenvectors
- Diagonalization
- Markov matrices
- Differential equations
- Symmetric matrices
- Positive definite matrices
- Matrices in engineering
- Similar matrices
- Singular value decomposition
- Fourier series, FFT, complex matrices
- Linear transformations
- Choice of basis
- Linear programming
- Course review
- Numerical linear algebra
- Computational science
Readings
- SES #: 1 · TOPICS: The geometry of linear equations · READINGS in 4th Edition: 1.1-2.1 · READINGS IN 5TH EDITION: 1.1-2.1
- SES #: 2 · TOPICS: Elimination with matrices · READINGS in 4th Edition: 2.2-2.3 · READINGS IN 5TH EDITION: 2.2-2.3
- SES #: 3 · TOPICS: Matrix operations and inverses · READINGS in 4th Edition: 2.4-2.5 · READINGS IN 5TH EDITION: 2.4-2.5
- SES #: 4 · TOPICS: LU and LDU factorization · READINGS in 4th Edition: 2.6 · READINGS IN 5TH EDITION: 2.6
- SES #: 5 · TOPICS: Transposes and permutations · READINGS in 4th Edition: 2.7 · READINGS IN 5TH EDITION: 2.7
- SES #: 6 · TOPICS: Vector spaces and subspaces · READINGS in 4th Edition: 3.1 · READINGS IN 5TH EDITION: 3.1
- SES #: 7 · TOPICS: The nullspace: Solving Ax = 0 · READINGS in 4th Edition: 3.2 · READINGS IN 5TH EDITION: 3.2
- SES #: 8 · TOPICS: Rectangular PA = LU and Ax = b · READINGS in 4th Edition: 3.3-3.4 · READINGS IN 5TH EDITION: 3.3
- SES #: 9 · TOPICS: Row reduced echelon form · READINGS in 4th Edition: 3.3-3.4 · READINGS IN 5TH EDITION: 3.3
- SES #: 10 · TOPICS: Basis and dimension · READINGS in 4th Edition: 3.5 · READINGS IN 5TH EDITION: 3.4
- SES #: 11 · TOPICS: The four fundamental subspaces · READINGS in 4th Edition: 3.6 · READINGS IN 5TH EDITION: 3.5
- SES #: 13 · TOPICS: Graphs and networks · READINGS in 4th Edition: 8.2 · READINGS IN 5TH EDITION: 3.5, 10.1
- SES #: 14 · TOPICS: Orthogonality · READINGS in 4th Edition: 4.1 · READINGS IN 5TH EDITION: 4.1
- SES #: 15 · TOPICS: Projections and subspaces · READINGS in 4th Edition: 4.2 · READINGS IN 5TH EDITION: 4.2
- SES #: 16 · TOPICS: Least squares approximations · READINGS in 4th Edition: 4.3 · READINGS IN 5TH EDITION: 4.3
- SES #: 17 · TOPICS: Gram-Schmidt and A = QR · READINGS in 4th Edition: 4.4 · READINGS IN 5TH EDITION: 4.4
- SES #: 18 · TOPICS: Properties of determinants · READINGS in 4th Edition: 5.1 · READINGS IN 5TH EDITION: 5.1
- SES #: 19 · TOPICS: Formulas for determinants · READINGS in 4th Edition: 5.2 · READINGS IN 5TH EDITION: 5.2
- SES #: 20 · TOPICS: Applications of determinants · READINGS in 4th Edition: 5.3 · READINGS IN 5TH EDITION: 5.3
- SES #: 21 · TOPICS: Eigenvalues and eigenvectors · READINGS in 4th Edition: 6.1 · READINGS IN 5TH EDITION: 6.1
- SES #: 22 · TOPICS: Diagonalization · READINGS in 4th Edition: 6.2 · READINGS IN 5TH EDITION: 6.2
- SES #: 23 · TOPICS: Markov matrices · READINGS in 4th Edition: 8.3 · READINGS IN 5TH EDITION: 10.3
- SES #: 26 · TOPICS: Differential equations · READINGS in 4th Edition: 6.3 · READINGS IN 5TH EDITION: 6.3
- SES #: 27 · TOPICS: Symmetric matrices · READINGS in 4th Edition: 6.4 · READINGS IN 5TH EDITION: 6.4
- SES #: 28 · TOPICS: Positive definite matrices · READINGS in 4th Edition: 6.5 · READINGS IN 5TH EDITION: 6.5
- SES #: 29 · TOPICS: Matrices in engineering · READINGS in 4th Edition: 8.1 · READINGS IN 5TH EDITION: 10.2
- SES #: 30 · TOPICS: Similar matrices · READINGS in 4th Edition: 6.6 · READINGS IN 5TH EDITION: 6.2
- SES #: 31 · TOPICS: Singular value decomposition · READINGS in 4th Edition: 6.7 · READINGS IN 5TH EDITION: 7.1-7.2
- SES #: 32 · TOPICS: Fourier series, FFT, complex matrices · READINGS in 4th Edition: 8.5, 10.2-10.3 · READINGS IN 5TH EDITION: 10.5, 9.2-9.3
- SES #: 33 · TOPICS: Linear transformations · READINGS in 4th Edition: 7.1-7.2 · READINGS IN 5TH EDITION: 8.1-8.2
- SES #: 34 · TOPICS: Choice of basis · READINGS in 4th Edition: 7.3 · READINGS IN 5TH EDITION: 8.3
- SES #: 35 · TOPICS: Linear programming · READINGS in 4th Edition: 8.4 · READINGS IN 5TH EDITION: 10.4
- SES #: 38 · TOPICS: Numerical linear algebra · READINGS in 4th Edition: 9.1-9.3 · READINGS IN 5TH EDITION: 11.1-11.3
Prerequisites & course information
Prereq: Calculus II (GIR) U (Spring) 4-0-8 units. REST Credit cannot also be received for 6.C06[J] , 18.700 , 18.C06[J] , CC.1806 , ES.1806
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Spring 2010
- MIT OCW readings ↗
- MIT OCW syllabus ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.