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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 cofactor/submatrix of a matrix
Definition of determinant of a matrix as a cofactor expansion across the first row
The determinant of a matrix can be computed as a cofactor expansion across any row.
The determinant of a matrix can be computed as a cofactor expansion down any column.
The inverse of a matrix can be expressed in terms of its matrix of cofactors.
Cramer's rule

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Definition of cofactor/submatrix of a matrixClose match
The determinant of a matrix can be computed as a cofactor expansion across any row.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 inverse of a matrix can be expressed in terms of its matrix of cofactors.Close match
Determinants and operations on matricesClose match
Cramer's ruleClose match
DeterminantsClose match
Notation for entry of matrixClose match
Determinants axiomaticallyClose match
A determinant is a multilinear functionClose match
Definition of coefficient matrix of a linear systemClose match
Basic terminology and notationClose match
Formula for the determinant of a 2-by-2 matrix.Close match
AdditionClose match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Operations on matricesClose match
MultiplicationClose match
ConjugationClose match
Definition of adjugate/classical adjoint of a matrixRelated

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