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15.2.11  Companion matrix of a polynomial

The companion command finds a matrix given its characteristic polynomial; specifically, if the polynomial is P(x)=xn+an−1xn−1+⋯+a−1x+a0, this matrix is equal to the identity matrix of size n−1 bordered with [0,0..,0,−a0] as first row, and with [−a0,−a1,…,−an−1] as last column.

Examples

companion(x^2+5x-7,x)
     


07
1−5


          
companion(x^4+3x^3+2x^2+4x-1,x)
     




0001
100−4
010−2
001−3




          

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