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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.
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  1. Definition of band matrix

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701–715 of 715 nodes
  • Triangular matrices#23561
  • Two matrices of the same size are equivalent if and only if they have the same rank.#23607
  • Two vectors are orthogonal if and only if the Pythagorean Theorem holds.#23918
  • Unitary matrices#23587
  • Unitary matrices are invertible.#23589
  • Unitary matrices have orthogonal (orthonormal) rows/columns.#23590
  • Unitary matrices preserve inner products.#23591
  • Unitary matrices preserve orthogonal (orthonormal) bases.#23592
  • Using matrices to solve linear systems#23760
  • Vector space isomorphism is an equivalence relation.#24003
  • Vector spaces#23775
  • Vector spaces with the same dimension are isomprphic.#24005
  • Vector sum/addition interpreted geometrically in R^n (or C^n)#23797
  • Vector sum/addition is commutative and associative#23787
  • Visualise a linear transformation on R^2 by looking at the image of a region#23852
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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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