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Thread: Finding a basis

  1. Oct 27th 2009, 08:09 PM #1
    amm345
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    Finding a basis

    Find a basis for Mmxn(F).

    I'm not sure how to approach this question, any help would be great.
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  2. Oct 28th 2009, 05:43 AM #2
    HallsofIvy
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    Starting with the definition of basis woud be good!

    Also, notice that
    \begin{bmatrix}a & b \\ c & d \end{bmatrix}= \begin{bmatrix}a & 0 \\ 0 & 0 \end{bmatrix}+ \begin{bmatrix}0 & b \\ 0 & 0\end{bmatrix}+ \begin{bmatrix}0 & 0 \\ c & 0\end{bmatrix}+ \begin{bmatrix}0 & 0 \\ 0 & d\end{bmatrix}

    = a\begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}+ b\begin{bmatrix}0 & 1 \\ 0 & 0\end{bmatrix}+ c\begin{bmatrix}0 & 0 \\ 1 & 0\end{bmatrix}+ d\begin{bmatrix}0 & 0 \\ 0 & 1\end{bmatrix}
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