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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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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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Determinants and operations on matrices

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Determinants multiply: det(AB) = det(A)det(B)Close match
DeterminantsClose 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
Operations on matricesClose match
A determinant is a multilinear functionClose match
Theorem describing the determinants of elementary matrices.Close 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
Determinants axiomaticallyClose match
Eigenvalues and operations on matricesClose match
Definition of determinant of a matrix as a cofactor expansion across the first rowClose 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 across any row.Close match
The permutation expansion for determinantsClose match
Formula for the determinant of a 2-by-2 matrix.Close match
The determinant of a block diagonal matrix is the product of the determinants of the blocks.Close match
Row operationsClose match
Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
The determinant of a matrix can be computed as a cofactor expansion down any column.Close match

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