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This question is related to the previous post, "A question about unitary and anti-unitary matrices". Following the suggestion of Lspice, I am posting it as a separate question, as it might ...

The question is the following: Let $U:\mathbf{C}^n\to \mathbf{C}^n$ be a unitary operator; let $\tilde{U}:\mathbf{C}^n\to\mathbf{C}^n$ be an antiunitary operator. Can one deform $U$ to $\tilde{U}$ ...