Transpose of Transpose of Matrix
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Theorem
Let $\mathbf A$ be a matrix.
Let $\mathbf A^\intercal$ be the transpose of $\mathbf A$.
Then:
- $\paren {\mathbf A^\intercal}^\intercal = \mathbf A$
Proof
Follows directly from the definition of the transpose of a matrix.
$\blacksquare$
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): transpose: $\text {(i)}$