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I have a square symmetrical matrix A (ugly I know)

321.1115, -57.5311, -33.9206

-57.5311, 296.7836, 10.8958

-33.9206, 10.8958, 382.1050

which has the eigen values,

248.8034

341.6551

409.5415

Am I right in saying that A when aligned with its eigen vectors it is,

248.8034, 0, 0

0, 341.6551, 0

0, 0, 409.5415

?

I would also like to transform the matrix so that,

A_{11}+A_{22}+A_{33}= 1

Thanks for any help, I feel like I should know this but have been running around in circles for the past 2 hours.

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# Aligning a matrix with its eigen vectors and other questions?

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