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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 left inverse of a matrix
  • Definition of right inverse of a matrix
  • Definition of inverse of a matrix
  • Definition of invertible matrix
  • If a matrix has both a left and a right inverse
  • If a square matrix has a one-sided inverse
  • Formula for the inverse of a 2-by-2 matrix.
  • Matrix inverse is an involution.
  • For n-by-n invertible matrices A and B
  • The product of square matrices is nonsingular if and only if each factor is nonsingular.
  • The inverse of a scalar multiple is the reciprocal times the inverse.
  • Matrix transpose commutes with matrix inverse.
  • The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.
  • Example of finding the inverse of a 2-by-2 matrix by row reducing the augmented matrix
  • Example of finding the inverse of a 2-by-2 matrix by using a formula
  • Example of finding the inverse of a 3-by-3 matrix by row reducing the augmented matrix
  • Example of finding the inverse of a 3-by-3 matrix by using Cramer's rule
  • The inverse of a matrix can be used to solve a linear system.
  • Matrix inverses are unique: if A and B are square matrices
  • Definition of generalized inverse of a matrix
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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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