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  • Particular types of matrices

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  • Echelon matrices
  • Definition of unit matrix
  • Definition of permutation matrix
  • Elementary matrices
  • Triangular matrices
  • Block matrices
  • Symmetric matrices
  • Nilpotent matrices
  • Definition of orthogonal matrix
  • Unitary matrices
  • Definition of band matrix
  • Definition of Vandermonde matrix
  • Definition of Markov matrix
  • Hermitian matrices
  • Normal matrices
  • The eigenvalues of a triangular matrix are the entries on the main diagonal.
  • A matrix with real entries has eigenvalues occurring in conjugate pairs.
  • Hermitian matrices have real eigenvalues.
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.
  • Definition of positive-definite matrix
  • Formula for the determinant of a 2-by-2 matrix.
  • Formula for the determinant of a 3-by-3 matrix.
  • The determinant of a triangular matrix is the product of the entries on the diagonal.
  • Theorem describing the determinants of elementary matrices.

Children5
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  • Definition of an upper triangular matrix
  • Definition of a lower triangular matrix
  • The product of upper/lower triangular matrices is upper/lower triangular.
  • The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.
  • Every square matrix is conjugate
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  1. Triangular matrices

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  • 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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