Transcription of Linear Algebra Review and Reference
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Linear Algebra Review and Reference
Linear Algebra Review and ReferenceZico Kolter (updated by Chuong Do and Tengyu Ma)June 20, 2020 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 of a Square Matrix .. Orthogonal Matrices .. Range and Nullspace of a Matrix .. The Determinant .. Quadratic Forms and Positive Semidefinite Matrices.
Jun 20, 2020 · As before, we can express yT in two obvious ways, depending on whether we express Ain terms on its rows or columns. In the rst case we express Ain terms of its columns, which gives yT = x TA= x 2 4 j j j a1 a 2 an j j j 3 5= x a1 xTa xTan which demonstrates that the ith entry of yT is equal to the inner product of xand the ith column of A.
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