An Interview with Gilbert Strang on Teaching Linear Algebra

Solving Ax=0 via Reduced Row Echelon Form to Find the Null Space Basis Linear Independence of Basis Vectors in Euclidean Space Linear Transformations in Linear Algebra Positive Definite Matrices and Quadratic Forms in Linear Algebra for Minimizing Functions Cramer's Rule: A Geometric Interpretation via Determinants and Volume Scaling Linear Transformations Preserving Addition and Scaling Operations Determinant Calculation for Square Matrices Incidence Matrices and Kirchhoff's Laws for Electrical Networks Matrix Multiplication Rules in Linear Algebra Markov Matrix Steady States and Fourier Series as Orthogonal Projections Dimension and Basis for Matrix Spaces from Symmetric Matrices to Small World Graphs Orthogonal Projection in Linear Algebra Eigenvalues of Symmetric, Skew-Symmetric, and Orthogonal Matrices in Linear Algebra Linear Systems of Equations in Linear Algebra Computing a Matrix Inverse Using Cofactors and the Determinant Formula in Linear Algebra Linear Algebra: Matrix Multiplication Rules and Gaussian Elimination to Find Inverse Matrices LU Factorization for Solving Linear Systems Eigenvalues, Orthogonal Projections, and Least Squares via Spectral Decomposition Linear Algebra Teaching Methods from Gilbert Strang Matrix Similarity in Linear Algebra Four Fundamental Subspaces in Linear Algebra Matrix-Vector Multiplication via Row-Column Dot Products and the Column Space Linear Algebra: Orthogonal Complements and Null Spaces Row Operations in Gaussian Elimination Algorithm Eigenvalues and Eigenvectors Definitions in Linear Algebra Image Compression Using Change of Basis and the Fourier Transform in JPEG Linear Algebra: Column Space and Nullspace of Matrices Eigenvalues and Eigenvectors in Linear Algebra Singular Value Decomposition via Eigenvalue Decomposition of A^TA and AA^T Gram-Schmidt Orthogonalization Algorithm Matrix-Vector Multiplication: Ax = b as a Linear Combination of Columns Matrix Similarity: A = PBP^-1 and Invariant Spectral Properties Eigenvalues and Eigenvectors for Symmetric Matrices Least Squares Estimation in Regression Analysis Projection Matrix Formulas in Linear Algebra Left and Right Inverses and the Pseudoinverse Rectangular Matrix Subspaces and Rank in Linear Algebra Orthogonal Projections in Linear Algebra Properties of Determinants Solution Sets of Ax=b and Ax=0: Affine Subspaces vs. the Null Space Matrix Determinant Calculation Methods in Linear Algebra Row Picture and Column Picture of a Linear System in Linear Algebra Row Exchanges and Permutation Matrices in PA=LU Factorization Hermitian and Unitary Matrices via the Fast Fourier Transform Solving Ax=b Using Gaussian Elimination and Back Substitution Determinant Calculation via Laplace Cofactor Expansion Along Any Row or Column Dimensions of the Null Space and Column Space via the Rank-Nullity Theorem Matrix Diagonalization: A = PDP^-1 via Eigenvectors and Eigenvalues Solving Linear Differential Equations via the Matrix Exponential exp(At)