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Matrices
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Basic terminology and notation
Operations on matrices
Particular types of matrices
Matrix equivalence
Canonical forms of matrices
Factorization of matrices
Similarity of matrices
Nonsingular matrices and equivalences
Rank and mullity
Eigenvalues and eigenvectors
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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