Let $B$ be a matrix. How can I tell which ($\mathrm{img}(B)$, $\mathrm{ker}(B^T)$, $\mathrm{img}(B^T)$) spaces are necessarily orthogonal to $\mathrm{ker}(B)$ under standard dot product?
What are the implications of orthogonality from dot product?
Let $B$ be a matrix. How can I tell which ($\mathrm{img}(B)$, $\mathrm{ker}(B^T)$, $\mathrm{img}(B^T)$) spaces are necessarily orthogonal to $\mathrm{ker}(B)$ under standard dot product?
What are the implications of orthogonality from dot product?
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