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 and b is a scalar then A^b is the matrix A to the power b.
• 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 (element-wise power). If A is a vector and b is a scalar then A^b and A.^b performs the same operation (i.e. element-wise power).
• 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)).
• 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.

Examples

A=[1 2;3 4];
A^2.5,
A.^2.5
(1:10)^2
(1:10).^2

s=`poly`_(0,'s')
s^(1:10)

See Also

• exp element-wise exponential
• hat (^) exponentiation