MATLAB Mathematics - SERC - Index of

1 Matrices and Linear Algebra
The LU factorization of A allows the linear system
A*x = b
to be solved quickly with
x = U\(L\b)
Determinants and inverses are computed from the LU factorization using
and
det(A) = det(L)*det(U)
inv(A) = inv(U)*inv(L)
You can also compute the determinants using det(A) = prod(diag(U)),
though the signs of the determinants may be reversed.
QR Factorization
An orthogonal matrix, or a matrix with orthonormal columns, is a real matrix
whose columns all have unit length and are perpendicular to each other. If Q
is orthogonal, then
Q′Q = 1
The simplest orthogonal matrices are two-dimensional coordinate rotations:
cos( θ)
sin( θ)
– sin( θ)
cos( θ)
For complex matrices, the corresponding term is unitary. Orthogonal and
unitary matrices are desirable for numerical computation because they
preserve length, preserve angles, and do not magnify errors.
The orthogonal, or QR, factorization expresses any rectangular matrix as the
product of an orthogonal or unitary matrix and an upper triangular matrix. A
column permutation may also be involved:
A
=
Q R
or
AP=
QR
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