(^,.^) power operation
t = A ^ b t = A ** b t = A .^ b
If an operand are encoded integers, the other one can be only encoded integers or real numbers.
If A
are polynomials or rationals, b
can only be
a single decimal (positive or negative) integer.
If A
or b
is scalar, it is first
replicated to the size of the other, with A*ones(b) or b*ones(A).
Otherwise, A
and b
must have the same size.
Then, for each element of index i, t(i) = A(i)^b(i)
is computed.
A
or b
must be a scalar,
and the other one must be a square matrix:
If A
is scalar and b
is
a square matrix, then A^b
is the matrix
expm(log(A) * b)
If A
is a square matrix and b
is scalar, then A^b
is the matrix
A
to the power b
.
For square matrices A^p
is computed through successive
matrices multiplications if p
is a positive integer, and by
diagonalization if not (see "note 2 and 3" below for details).
If A
is a square and Hermitian matrix and p
is a non-integer scalar, A^p
is computed as:
A^p = u*diag(diag(s).^p)*u'
(For real matrix A
,
only the real part of the answer is taken into account).
u
and s
are determined by
[u,s] = schur(A)
.
If A
is not a Hermitian matrix and p
is a
non-integer scalar, A^p
is computed as:
A^p = v*diag(diag(d).^p)*inv(v)
(For real matrix A
,
only the real part of the answer is taken into account).
d
and v
are determined by
[d,v] = bdiag(A+0*%i)
.
If A
and p
are real or complex numbers,
A^p
is the principal value determined by
If A
is a square matrix and p
is a real or
complex number, A.^p
is the principal value
computed as:
**
and ^
operators are synonyms.
![]() | Exponentiation is right-associative in Scilab, contrarily to MatlabĀ® and Octave.
For example 2^3^4 is equal to 2^(3^4) in Scilab, but to (2^3)^4 in MatlabĀ® and Octave. |
Version | Description |
6.0.0 | With decimal or complex numbers, scalar ^ squareMat now
yields expm(log(scalar)*squareMat) instead of
scalar .^ squareMat |