- #1
libelec
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Homework Statement
Prove that the Unitary matrixes are the only ones that preserve the length of the vectors.
The Attempt at a Solution
It's an iff, so I have to prove that a) If the matrix is Unitary, then it preserves the length and b) If the matrix preserves the length, then it's Unitary
I could only solve a) (using the canonic inner product for R)
Let it be A [tex]\in[/tex] [tex]\Re[/tex]nXn an unitary matrix, x [tex]\in[/tex] [tex]\Re[/tex]n, then (Ax, Ax) = (Ax)T(Ax) = xTATAx = xTx, because ATA = I, for A is unitary, then xTx = (x,x). Then, A preserves the length.
But I don't know how to prove b).