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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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The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.

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The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.Close match
DeterminantsClose match
A determinant is a multilinear functionClose match
Definition of the determinant in terms of the effect of elementary row operationsClose match
A matrix and its transpose have the same determinant.Close match
Determinants and operations on matricesClose match
Theorem describing the determinants of elementary matrices.Close match
The determinant of a triangular matrix is the product of the entries on the diagonal.Close match
Determinants axiomaticallyClose match
The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.Close match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
The determinant of a matrix can be computed as a cofactor expansion down any column.Close match
Definition of determinant of a matrix as a cofactor expansion across the first rowClose match
The determinant of a block diagonal matrix is the product of the determinants of the blocks.Close match
Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
A matrix with two equal rows/columns has determinant 0Close match
The determinant of a matrix can be computed as a cofactor expansion across any row.Close match
Formula for the determinant of a 2-by-2 matrix.Close match
Definition of trace of a matrixRelated

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