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  • Operations on matrices

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  • Addition
  • Conjugation
  • Scalar multiplication
  • Row operations
  • Matrix-vector products
  • Multiplication
  • Transpose and adjoint
  • Inverse

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  • Definition of matrix multiplication in terms of column vectors
  • Definition of matrix multiplication
  • Theorem describing matrix multiplication
  • Any matrix times the 0 matrix equals the 0 matrix.
  • Example of multiplying 2x2 matrices
  • Example of multiplying 3x3 matrices
  • Example of multiplying nonsquare matrices
  • Example of multiplying matrices
  • Matrix multiplication is associative.
  • Matrix multiplication is distributive over matrix addition.
  • The identity matrix is the identity for matrix multiplication.
  • Matrix multiplication is not commutative in general.
  • For matrices
  • Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectors
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  1. Multiplication

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251–275 of 715 nodes
  • Definition of orthogonal subspaces#24094
  • Definition of orthogonal vectors#23916
  • Definition of orthonormal basis of a (sub)space#23929
  • Definition of orthonormal set of vectors#23926
  • Definition of parallel vectors#23917
  • Definition of permutation matrix#23555
  • Definition of pivot#23476
  • Definition of pivot column#23477
  • Definition of pivot position#23478
  • Definition of positive-definite matrix#23713
  • Definition of pre-image (of a point) under a linear transformation#23843
  • Definition of pre-image of linear transformation#24019
  • Definition of QR decomposition#23631
  • Definition of quadratic form#24122
  • Definition of range of a linear transformation#24020
  • Definition of range of linear transformation#23846
  • Definition of rank factorization of a matrix#23628
  • Definition of rank of a linear transformation#23883
  • Definition of rank of a matrix#23674
  • Definition of rational form#23621
  • Definition of reduced LU decomposition#23627
  • Definition of reduced row echelon form of a matrix#23544
  • Definition of right inverse of a matrix#23516
  • Definition of R^n (or C^n)#23781
  • Definition of (row) echelon form of a matrix#23542
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