20 Let h(x) n i 0 a i x i be a polynomial Define h(A) by h(A) n i 0 a i A i where A 0 I and a i are scalars If 1 , 2 , , n are the characteristic roots of the n x n matrix A, show that tr h(A) n i 1 h( i ) ...

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20. Let h(x) = n i=0 a i x i be a polynomial. Define h(A) by...

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20. Let h(x) = Σⁿ_i=0 a_ixⁱ be a polynomial. Define h(A) by h(A)= Σⁿ_i=0 a_iAⁱ.

where A⁰ = I and a_i are scalars. If λ₁, λ₂, ..., λ_n are the characteristic roots of the n x n matrix A, show that tr [h(A)] = Σⁿ_i=1 h(λ_i).

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Matrices With Applications In Statistics

ISBN: 9780534980382

2nd Edition

Authors: Franklin A Graybill

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Question Posted: Sep 19, 2024 07:03 AM

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20. Let h(x) = n i=0 a i x i be a polynomial. Define h(A) by...

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Matrices With Applications In Statistics

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