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18.06 Linear Algebra
18 topics, 24 prerequisite links. The keystones — Linear Systems and Gaussian Elimination (14), Four Fundamental Subspaces (11), Matrix Algebra and Inverses (8) — have the most topics resting on them.
Not practisedStrugglingLearningMastered· ✓ = you marked it done
All topics in learning order
- ✓ Linear Systems and Gaussian Elimination — starting point
- Matrix Algebra and Inverses — needs Linear Systems and Gaussian Elimination
- ✓ Vector Subspaces — starting point
- Four Fundamental Subspaces — needs Linear Systems and Gaussian Elimination
- ✓ Linear Independence and Span — needs Vector Subspaces
- Basis and Dimension — needs Linear Independence and Span, Four Fundamental Subspaces
- Linear Transformations and Matrix Representations — needs Basis and Dimension, Matrix Algebra and Inverses
- Inner Products and Norms — starting point
- Orthogonal Subspaces and Complements — needs Inner Products and Norms, Four Fundamental Subspaces
- Projections and Least Squares — needs Orthogonal Subspaces and Complements
- Gram-Schmidt and QR Factorization — needs Inner Products and Norms, Projections and Least Squares
- Determinants and Properties — needs Matrix Algebra and Inverses
- Eigenvalues and Eigenvectors — needs Determinants and Properties, Four Fundamental Subspaces
- Matrix Diagonalization — needs Eigenvalues and Eigenvectors, Basis and Dimension
- Symmetric Matrices and Spectral Theorem — needs Matrix Diagonalization, Gram-Schmidt and QR Factorization
- Positive Definite Matrices — needs Symmetric Matrices and Spectral Theorem
- Singular Value Decomposition (SVD) — needs Symmetric Matrices and Spectral Theorem, Projections and Least Squares
- Engineering Applications — needs Singular Value Decomposition (SVD), Projections and Least Squares