Transcription of LinearAlgebraReviewandReference
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Linear Algebra Review and ReferenceZico Kolter (updated by Chuong Do)September 30, 2015 Contents1 Basic Concepts and Basic Notation .. 22 matrix Vector-Vector Products .. matrix -Vector Products .. matrix - matrix Products .. 53 Operations and The Identity matrix and Diagonal Matrices .. The Transpose .. Symmetric Matrices .. The Trace .. Norms .. Linear Independence and Rank .. The Inverse .. Orthogonal Matrices .. Range and Nullspace of a matrix .. The Determinant .. Quadratic Forms and Positive Semidefinite Matrices .. Eigenvalues and Eigenvectors.
2 Matrix Multiplication The product of two matrices A ∈ Rm×n and B ∈ Rn×p is the matrix C = AB ∈ Rm×p, where Cij = Xn k=1 AikBkj. Note that in order for the matrix product to exist, the number of columns in A must equal the number of rows in B. There are many ways of looking at matrix multiplication, and we’ll start by examining a ...
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