Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
power
(^,.^) power operation
Calling Sequence
t=A^b t=A**b t=A.^b
Arguments
- A,t
scalar, polynomial or rational matrix.
- b
a scalar, a vector or a scalar matrix.
Description
If
A
is a square matrix andb
is a scalar thenA^b
is the matrixA
to the powerb
.If
b
is a scalar andA
a matrix thenA.^b
is the matrix formed by the element ofA
to the powerb
(element-wise power). IfA
is a vector andb
is a scalar thenA^b
andA.^b
performs the same operation (i.e. element-wise power).If
A
is a scalar andb
is a matrix (or vector)A^b
andA.^b
are the matrices (or vectors) formed bya^(b(i,j))
.If
A
andb
are vectors (matrices) of the same sizeA.^b
is theA(i)^b(i)
vector (A(i,j)^b(i,j)
matrix).
Additional Remarks
Notes: |
1. 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).
2. 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)
.
3. 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)
.
4. If A
and p
are real or complex numbers,
A^p
is the principal value determined by:
A^p = exp(p*log(A))
(or A^p = exp(p*(log(abs(A))+ %i*atan(imag(A)/real(A))))
).
5. If A
is a square matrix and p
is a real or complex number,
A.^p
is the principal value computed as:
A.^p = exp(p*log(A))
(same as case 4 above).
6. **
and ^
operators are synonyms.
Examples
Report an issue | ||
<< plus | Scilab keywords | quote >> |