Let A be an n n diagonal matrix with diagonal entries 1, 2, , n where, i 0i Show that there exists an n n diagonal matrix B such that B2 A

Question: Let A be an n n diagonal matrix with diagonal entries 1, 2, . . . , n where, i 0i. Show that

Let A be an n × n diagonal matrix with diagonal entries λ1, λ2, . . . , λn where, λi ≥ 0∀i. Show that there exists an n × n diagonal matrix B such that B2 = A.

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