1. Let T : Mn×n(F) → Mn×n(F) be the transposition map, T(A) = At. Compute the...

1. Let T : Mn×n(F) → Mn×n(F) be the transposition map, T(A) = At. Compute the characteristic polynomial of T. You may wish to use the basis of Mn×n(F) consisting of the matrices eij + eji, eij −eji and eii.

2. Let A = (a b c d) (2 by 2 matrix) and let T : M2×2(F) → M2×2(F) be deﬁned asT (B) = AB. Represent T as a 4×4 matrix using the ordered basis {e11,e21,e12,e22}, and use this matrix to prove that the characteristic polynomial of T is the square of the characteristic polynomial of A.

Expert Solution

Colby Messinger answered 2 years ago

Let F be a field and R = Mn(F) the ring of n×n matrices with entires...

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a) write a program to compute and print n, n(f), f(f(n)), f(f(f(n))).........for 1<=n<=100, where f(n)=n/2 if...

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proof: L t^(n+1)f(t)=(-1)^(n+1)(d^(n+1)/ds^(n+1))*F(s)

proof: L t^(n+1)*f(t)=(-1)^(n+1)*(d^(n+1)/ds^(n+1))*F(s)

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