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LinearAlgebraReviewandReference

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.

If so, take the time to check it for yourself! Second, we can also view matrix-matrix multiplication as a set of matrix-vector products. Specifically, if we represent B by columns, we can view the columns of C as matrix-vector products between A and the columns of B. Symbolically,

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