HW9_f07

# HW9_f07 - 3) Find the square root of : You must first...

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AME 525 Homework 9 due at classtime, Wednesday October 31 1) Consider a new basis given by the orthogonal unit vectors: () 1 , 0 , 0 , 0 , 2 1 , 2 1 , 0 , 2 1 , 2 1 Find the representation in the new basis of the matrix: 9 8 7 6 5 4 3 2 1 2) By direct calculation (i.e. without first finding the eigenvalues) find the three invariants of: 5 0 4 0 3 0 6 4 2 Now calculate the eigenvalues and use the result to check you answer.
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Unformatted text preview: 3) Find the square root of : You must first diagonalize the matrix, then take the square root of every element and then transform back to the original space. (Use only positive roots for the eigenvalues.) 4) Show by direct calculation that the matrix in Problem 3 satisfies its own characteristic equation. 3 4 4 3...
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