power — power operation (^,.^)
t=A^b t=A**b t=A.^b
"(A:square)^(b:scalar)"
If A
is a square matrix and b
is a scalar then A^b
is the matrix A
to the power b
.
"(A:matrix).^(b:scalar)"
If b
is a scalar and A
a matrix then
A.^b
is the matrix formed by the element of
A
to the power b
(elementwise power). If
A
is a vector and b
is a scalar then
A^b
and A.^b
performs the same operation
(i.e elementwise power).
"(A:scalar).^(b:matrix)"
If A
is a scalar and b
is a matrix (or vector) A^b
and A.^b
are the matrices (or vectors) formed by a^(b(i,j))
.
"(A:matrix).^(b:matrix)"
If A
and b
are vectors (matrices) of the same size A.^b
is the A(i)^b(i)
vector (A(i,j)^b(i,j)
matrix).
Notes:
-
For square matrices A^p
is computed through successive
matrices multiplications if p
is a positive integer, and by
diagonalization if not.
-
**
and ^
operators are synonyms.