On Tuesday, December 18, 2012 11:45:47 AM UTC-8, projetmbc wrote:
>
> Hello,
> in the following code I would like to replace x with T in Delta_X so as to
> illustrate
> the Cayley Hamilton theorem by doing everything by hands.
>
> Is it possible ?
>
> Best regards.
> Christophe BAL
>
> =========================
> var('a b c d e f')
>
> T = matrix([
> [a, b, c],
> [0, d, e],
> [0, 0, f]
> ])
>
> T_X = T - x*identity_matrix(3)
>
> Delta_X = det(T_X)
>
I can't get that to work. However, this does: treat the variables as
polynomial indeterminates instead of symbolic variables.
sage: R.<a,b,c,d,e,f,x> = QQ[]
sage: T = matrix([
[a, b, c],
[0, d, e],
[0, 0, f]
])
sage: T_X = T - x*identity_matrix(3)
sage: Delta_X = det(T_X)
sage: Delta_X.subs(x=T)
[0 0 0]
[0 0 0]
[0 0 0]
--
John
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