MIT
Lecture 2: Multiplying and Factoring Matrices
Science & MathMathematicsEngineeringElectrical Engineering
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Description Multiplying and factoring matrices are the topics of this lecture. Professor Strang reviews multiplying columns by rows: \(AB =\) sum of rank one matrices. He also introduces the five most important factorizations. Summary Multiply columns by rows: \(AB =\) sum of rank one matrices Five great factorizations: \(A = LU\) from elimination \(A = QR\) from orthogonalization (Gram-Schmidt) \(S = Q \Lambda Q^{\mathtt{T}}\) from eigenvectors of a symmetric matrix \(S\) \(A = X \Lambda X^{-1}\) diagonalizes \(A\) by the eigenvector matrix \(X\) \(A = U \Sigma V^{\mathtt{T}} =\) (orthogonal)(diagonal)(orthogonal) = Singular Value Decomposition Related section in textbook: I.2 Instructor: Prof. Gilbert Strang