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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

Children20
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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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451–475 of 715 nodes
  • Geometric properties of R^n (or C^n)#23795
  • Hermitian matrices#23596
  • Hermitian matrices have real eigenvalues.#23711
  • Homogeneous linear systems are consistent.#23434
  • If A and B are n-by-n matrices#23729
  • If A is a matrix#23679
  • If a matrix has both a left and a right inverse#23519
  • If a set of vectors contains the 0 vector#23825
  • If a set of vectors in R^n (or C^n) contains more than n elements#23827
  • If a space is the direct sum of invariant subspaces#24053
  • If a square matrix has a one-sided inverse#23520
  • If a vector space has dimension n#23838
  • If B is a basis containing b and the b coordinate of c is nonzero#23990
  • If the product of a vector and a scalar is 0#23962
  • If two finite dimensional subspaces have the same dimension and one is contained in the other#24011
  • If two matrices have equal products with all vectors#23484
  • Inner products#24087
  • Inner products in coordinate spaces#23894
  • Inverse#23514
  • Isomorphic vector spaces have the same dimension.#24004
  • Isomorphism#24000
  • Least squares#23945
  • Linear algebra#23410
  • Linear combinations#23799
  • Linear (in)dependence#23815
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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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