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  • Triangular matrices

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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 complex square matrix is unitarily similar to an upper triangular matrix
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  1. The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.

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  • The product of upper/lower triangular matrices is upper/lower triangular.Close match
  • Triangular matricesClose match
  • Definition of an upper triangular matrixClose match
  • Definition of a lower triangular matrixClose match
  • InverseClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Definition of invertible matrixClose match
  • The determinant of a triangular matrix is the product of the entries on the diagonal.Close match
  • Equivalence theorem for nonsingular matrices: the transpose of the matrix A has an inverse.Close match
  • Definition of inverse of a linear transformationClose match
  • Elementary matrices are invertible/nonsingular.Close match
  • The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
  • Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Close match
  • Unitary matrices are invertible.Close match
  • Equivalence theorem for nonsingular matrices: the matrix A has a right inverse.Close match
  • Equivalence theorem for nonsingular matrices: the matrix A has a left inverse.Close match
  • The eigenvalues of a triangular matrix are the entries on the main diagonal.Close match
  • A nonsingular matrix can be written as a product of elementary matrices.Close match
  • Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax has an inverse.Close match
  • Definition of invertible linear transformationClose match

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