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Evaluating A Descending Polynomial Using Matrix Multiplication
Syntax polyvalm(px)
See Also polyval , polval

Description
Returns the evaluation of the descending polynomial corresponding to p at the square matrix x. The return value is
                n-1                 1            0
     p[x] = p  x     + ... +  p    x     +  p   x
             1                 n-1           n
where n is the length of the vector p and
      0                                  i+1        i
     x  = I  and for i = 2, ... , n-1,  x    = x * x 
where * denotes matrix multiplication and I denotes the identity matrix with same dimensions as x. The integer, real, double-precision, or complex vector p specifies the polynomial to be evaluated. The integer, real, double-precision, or complex matrix x specifies the argument to the polynomial. The return matrix has the same dimension as x and the same type as a binary operation between p and x. (See the coercion entry in the O-Matrix User's Guide.)

Example
If you enter
     p = [1, 1, 1]
     x = { ...
         [ 1 , -1 ], ...
         [ 0 ,  1 ] ...
     }
     polyvalm(p, x)
O-Matrix will reply
     {
     [ 3 , -3 ]
     [ 0 , 3 ]
     }
If you continue by entering
     x * x  +  x  +  identity(2)
O-Matrix will reply
     {
     [ 3 , -3 ]
     [ 0 , 3 ]
     }