Solve the general linear matrix equation
for matrix
:
a and
b are nonsingular matrices:
The Kronecker product is also nonsingular:
The inverse of the product can be computed from the simpler inverses of
a and
b:
s is a differentiation matrix approximating the second derivative in 1 dimension:
The identity matrix as a sparse array:
A two-dimensional array of values:
A matrix that differentiates in the first dimension only:
A matrix that approximates the Laplacian:
Define the
n×n "bit reversal" permutation matrix for
n a power of 2:
A compact notation for the identity matrix of size
n:
A compact notation for the direct matrix product:
Form the discrete Fourier transform matrix for length 16 from the Cooley-Tukey factorization:
r is a random vector of length 16:
The discrete Fourier transform of
r:
Fourier is fast because it effectively composes the factorization for a particular vector:
EXAMPLES
Basic Examples 
Scope 
