Polynomial to companion matrix

Given the polynomial $p left parenthesis x right parenthesis equals a subscript 0 plus a subscript 1 t plus midline horizontal ellipsis plus a subscript n minus 1 end subscript t to the power of n minus 1 end exponent plus a subscript n t to the power of n$ the companion matrix is the square matrix defined as

$C left parenthesis p right parenthesis space equals space open parentheses table row 0 0 midline horizontal ellipsis 0 cell negative c subscript 0 end cell row 1 0 midline horizontal ellipsis 0 cell negative c subscript 1 end cell row 0 1 midline horizontal ellipsis 0 cell negative c subscript 2 end cell row vertical ellipsis vertical ellipsis down right diagonal ellipsis vertical ellipsis vertical ellipsis row 0 0 midline horizontal ellipsis 1 cell negative c subscript n minus 1 end subscript end cell end table close parentheses$

where $c subscript i equals a subscript i over a subscript n$ .

polynomial_to_companion_matrix(Polynomial)

Description

polynomial_to_companion_matrix(Polynomial)

Given a polynomial, returns the companion matrix as described above.

Matrix

Polynomial to companion matrix

Syntax

Description

polynomial_to_companion_matrix(Polynomial)

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