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List of matrices
Listed below are some important classes of
matrices
used in
mathematics
:
Diagonal matrix
- All entries not on the main diagonal (the diagonal from the upper left to the lower right corner) are zero. Especially easy to raise to a power.
Diagonalizable matrix
- A matrix
similar
to a diagonal matrix. It has a complete set of linearly independent
eigenvectors
.
Normal matrix
- It has a complete set of
orthonormal
eigenvectors.
Symmetric matrix
- A matrix that is its own
transpose
.
Hermitian matrix
- A matrix that is its own
conjugate transpose
. It is a normal matrix.
Positive definite matrix
- Hermitian matrix with every
eigenvalue
positive.
Orthogonal matrix
- A matrix which has the same
inverse
and
transpose
, can represent a rotation.
Unitary matrix
- A matrix whose
conjugate transpose
is its
inverse
.
Positive matrix[?]
- A matrix with all numbers ≥ 0.
Totally positive matrix[?]
-
Determinants
of all its square submatrices are positive. It is used in generating the reference points of
Bézier curve
in
computer graphics
.
Stochastic matrix
- A positive matrix describing a
stochastic process
. The sum of entries of any row is one.
Permutation matrix
- Matrix representation of a
permutation
.
Toeplitz matrix
Vandermonde matrix[?]
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