Evaluating a Polynomial with a Matrix

The matrix evaluation of a polynomial differs from 2D polynomial evaluation.

When performing matrix evaluation of a polynomial, you must use a square matrix. The following equations define a second-order polynomial P(x) and a square 2 × 2 matrix G.

In 2D polynomial evaluation, you evaluate P(x) at each element of matrix G, as shown by the following equation.

When performing matrix polynomial evaluation, you replace the variable x with matrix G, as shown by the following equation.

where I is the identity matrix of the same size as G.

In the following equations, actual values replace the variables a and g in the previous equations that define a second-order polynomial P(x) and a square 2 × 2 matrix G.

P(x) = 5 + 3x +2x

The following equation shows the matrix evaluation of the polynomial P(x) from the first equation above with matrix G from the second equation above.