Let A be an n×n matrix with n different positive eigenvalues. Prove that there exists a matrix B such that B2 = A. Is B uniquely determined? Please do this step by step in detail, show why you are allowed to take certain steps, I often have problems finding the right theorem to apply.

Let A be an n×n matrix with n different positive eigenvalues. Prove that there exists a matrix B such that B2 = A. Is B uniquely determined? Please do this step by step in detail, show why you are allowed to take certain steps, I often have problems finding the right theorem to apply.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let A be an n×n matrix with n different positive eigenvalues. Prove that there exists a matrix B such that B² = A. Is B uniquely determined?

Please do this step by step in detail, show why you are allowed to take certain steps, I often have problems finding the right theorem to apply.

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