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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 multilinear function
The determinant function exists.
The determinant function is unique.
A determinant is a multilinear function
Adding a multiple of one row to another row does not change the determinant.
Switching two rows multiplies the determinant by -1.
Multiplying a row by a scalar multiplies the determinant by that scalar.
A matrix with two equal rows/columns has determinant 0
A matrix with a 0 row/column has determinant 0
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11 December 2017, 11:08 (UTC+00:00)
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