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Parents1

  • Determinants

Siblings10
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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 determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.
  • The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.
  • Definition of the determinant in terms of the effect of elementary row operations
  • The permutation expansion for determinants
  • A matrix and its transpose have the same determinant.
  • If A and B are n-by-n matrices
  • The determinant of the inverse of A is the reciprocal of the determinant of A.
  • The determinant of a block diagonal matrix is the product of the determinants of the blocks.
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