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.TH power 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
power - power operation (^,.^)
.SH CALLING SEQUENCE
.nf
t=A^b
t=A**b
t=A.^b
.fi
.SH PARAMETERS
.TP
A,t
: scalar, polynomial or rational matrix.
.TP
b
:a scalar, a vector or a scalar matrix.
.SH DESCRIPTION
.TP
(A:square)^(b:scalar)
: If \fVA\fR is a square matrix and \fVb\fR is a scalar then
\fVA^b\fR is the matrix \fVA\fR to the power \fVb\fR.
.TP
(A:matrix).^(b:scalar)
: If \fVb\fV is a scalar and \fVA\fR a matrix then \fVA.^b\fR
is the matrix formed by the element of \fVA\fR to the power \fVb\fR (elementwise power). If \fVA\fR is a vector and \fVb\fR is a scalar then
\fVA^b\fR and \fVA.^b\fR performs the same operation (i.e elementwise power).
.TP
(A:scalar).^(b:matrix)
If \fVA\fR is a scalar and \fVb\fR is a scalar matrix (or vector) \fVA^b\fR and
\fVA.^b\fR are the matrices (or vectors) formed by \fV a^(b(i,j))\fR.
.TP
(A:matrix).^(b:matrix)
If \fVA\fR and \fVb\fR are vectors (matrices) with compatible dimensions
\fVA.^b\fR is the \fVA(i)^b(i)\fR vector (\fVA(i,j)^b(i,j)\fR matrix).
.LP
Notes:
.IP -
For square matrices \fVA^p\fR is computed through successive
matrices multiplications if \fVp\fR is a positive integer, and by
diagonalization if not.
.IP -
\fV**\fR and \fV^\fR operators are synonyms.
.SH EXAMPLE
.nf
A=[1 2;3 4];
A^2.5,
A.^2.5
(1:10)^2
(1:10).^2
s=poly(0,'s')
s^(1:10)
.fi
.SH SEE ALSO
exp
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