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  • Determinants

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  • Particular types of matrices
  • Definition of trace of a matrix
  • Cofactors
  • Determinants and operations on matrices
  • Determinants axiomatically
  • The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.
  • The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.
  • Definition of adjugate/classical adjoint of a matrix
  • A matrix is called ill-conditioned if it is nearly singular
  • The condition number of matrix measures how close it is to being singular

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  • Definition of cofactor/submatrix of a matrix
  • Definition of determinant of a matrix as a cofactor expansion across the first row
  • The determinant of a matrix can be computed as a cofactor expansion across any row.
  • The determinant of a matrix can be computed as a cofactor expansion down any column.
  • The inverse of a matrix can be expressed in terms of its matrix of cofactors.
  • Cramer's rule
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  1. Cofactors

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501–525 of 715 nodes
  • Matrix transpose commutes with matrix inverse.#23526
  • Matrix transpose is an involution.#23504
  • Matrix-vector multiplication is a linear transformation.#23856
  • Matrix-vector product is associative#23486
  • Matrix-vector products#23482
  • Multiplication#23487
  • Multiplication by a change of coordinates matrix converts representations for different bases.#23997
  • Multiplication by a Hermitian matrix commutes with the standard inner product on C^n.#23598
  • Multiplication of block/partitioned matrices#23569
  • Multiplicity#23695
  • Multiplying a row by a scalar multiplies the determinant by that scalar.#23739
  • Nilpotent matrices#23580
  • Non-example of a linear transformation#23850
  • Nonsingular matrices and equivalences#23640
  • Normal matrices#23599
  • Norm and length#23907
  • Notation for entry of matrix#23450
  • Notation for the set of m by n matrices#23453
  • Operations on matrices#23460
  • Orthogonality#23914
  • Orthogonality and projection#23893
  • Parametric form of the solution set of a system of linear equations#23419
  • Parametric vector form of the solution set of a system of linear equations#23420
  • Particular types of matrices#23535
  • Projection#23937
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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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