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Determinants and operations on matrices

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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.
Determinants multiply: det(AB) = det(A)det(B)
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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The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.

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Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
Determinants and operations on matricesClose match
A matrix and its transpose have the same determinant.Close match
The determinant of a block diagonal matrix is the product of the determinants of the blocks.Close match
A determinant is a multilinear functionClose match
Definition of the determinant in terms of the effect of elementary row operationsClose match
The determinant of a triangular matrix is the product of the entries on the diagonal.Close match
Theorem describing the determinants of elementary matrices.Close match
Determinants multiply: det(AB) = det(A)det(B)Close match
LU decompositionClose match
Definition of LU decompositionClose match
Triangular matricesClose match
DeterminantsClose match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Definition of an upper triangular matrixClose match
A matrix with two equal rows/columns has determinant 0Close match
Determinants axiomaticallyClose match
Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
Switching two rows multiplies the determinant by -1.Close match
The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.Close match

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