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  • Determinants

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  • Particular types of matrices
  • Definition of trace of a matrix
  • 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
  • Determinants and operations on matrices
  • Cofactors
  • Ill-conditioning is measured by relative distance to singularity
  • Condition number measures relative sensitivity
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  1. Definition of adjugate/classical adjoint of a matrix

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  • Definition of adjoint (conjugate transpose)Close match
  • The inverse of a matrix can be expressed in terms of its matrix of cofactors.Close match
  • Matrix adjoint is an involution.Close match
  • The adjoint of a matrix-scalar product is the product of the adjoint and the conjugate.Close match
  • Transpose and adjointClose match
  • Definition of conjugate of a matrixClose match
  • The adjoint of a product of matrices is the product of the adjoints in reverse order.Close match
  • A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.Close match
  • The adjoint of a sum is the sum of the adjoints.Close match
  • Definition of cofactor/submatrix of a matrixClose match
  • Definition of transpose of a matrixClose match
  • Definition of determinant of a matrix as a cofactor expansion across the first rowClose match
  • ConjugationClose match
  • The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
  • Definition of Hermitian/self-adjoint matrixClose match
  • The conjugate of the transpose is the transpose of the conjugate.Close match
  • Determinants and operations on matricesClose match
  • Determinants axiomaticallyClose match
  • The transpose of a product of matrices is the product of the transposes in reverse order.Close match
  • InverseClose match

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