Let A be the real 2x2 matrix
with bc greater than or equal to 0. Prove there exists a real 2x2 invertible matrix S so that S^-1 A S is either diagonal or of the form
where x is the eigenvalue of A.
Please see the attachment.
First, we set . We consider the following cases.
1. . Without loss of generality, we can assume . Let . Since . If , then has two distinct zero points and . If , then we note , , . According to the ...
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