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Math Help - Why is this set a subspace ??

  1. #1
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    Why is this set a subspace ??

    Why is the following set a subspace of M_{n \times n}^R, n \geq 2

    B = \{A \in M_{n \times n}^C | A_\downarrow_1 = (1-2i)A_\downarrow_2 \}

    I immediately said it is not a subspace since complex numbers aren't in real numbers. It's the other way around. But I am wrong apparently...
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  2. #2
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    Quote Originally Posted by jayshizwiz View Post
    Why is the following set a subspace of M_{n \times n}^R, n \geq 2

    B = \{A \in M_{n \times n}^C | A_\downarrow_1 = (1-2i)A_\downarrow_2 \}

    I immediately said it is not a subspace since complex numbers aren't in real numbers. It's the other way around. But I am wrong apparently...
    This is NOT a vector space over the real numbers but it IS a vector space over the complex numbers, Just as the original space, M_{nxn}^C is a vector space over the complex numbers, not the real numbers.
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  3. #3
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    This is NOT a vector space over the real numbers but it IS a vector space over the complex numbers, Just as the original space, is a vector space over the complex numbers, not the real numbers.
    So is it a mistake that the question says it is a subspace over M_{n \times n}^R
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