In the last equal sign of the last line below, why is ? Thanks. Given the DE system where is n-vector, is an nxn matrix, and is a an eigenvector of A, let , then .
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Originally Posted by MSUMathStdnt In the last equal sign of the last line below, why is ? Thanks. Given the DE system where is n-vector, is an nxn matrix, and is a an eigenvector of A, let , then . Look back to the first of the line. What the first to the next to last term shows is that because v is a constant.
Originally Posted by HallsofIvy Look back to the first of the line. What the first to the next to last term shows is that because v is a constant. I'm not sure what you're trying to tell me. I understand that is constant. But how does what you wrote mean that ? Is it because , ( being the identity matrix), which would make the right side of this into the left side of the given system with as and as ?
Yes,. if for any (non-zero) vector, v, av= bv, then a= b.
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