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Determinants
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Particular types of matrices
Definition of trace of a matrix
Cofactors
Determinants and operations on matrices
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
A matrix is called ill-conditioned if it is nearly singular
The condition number of matrix measures how close it is to being singular
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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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Container for Linear Algebra
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Determinants
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Cofactors
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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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