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Mathematics
Linear and Abstract Algebra
Does a unitary matrix have such property?
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[QUOTE="Haorong Wu, post: 6184103, member: 658919"] [B]TL;DR Summary:[/B] I need prove a property of unitary matrices, but without success. Hi. I'm learning Quantum Calculation. There is a section about controlled operations on multiple qubits. The textbook doesn't express explicitly but I can infer the following statement: [B]If ##U## is a unitary matrix, and ##V^2=U##, then ## V^ \dagger V=V V ^ \dagger=I##. [/B] I had hard time proving it. I only can prove that if ##V## is reversible, then ##\left (V^ \dagger V \right ) \left ( V V ^ \dagger \right )=I##. I hope the statement is true, otherwise my inference would be wrong. [/QUOTE]
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Mathematics
Linear and Abstract Algebra
Does a unitary matrix have such property?
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