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Jiahao Chen added Apostol_s_Calculus_defines_the__.tex
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Apostol's Calculus defines the matrix transpose elementwise, which is perhaps the more familiar form
Vol 2, p. 91:
\begin{definition}
The transpose of an $m \times n$ matrix $A = \left( a_{ij} \right)^{m,n}_{i,j=1} is the $n \times m$ matrix $A^t$ whose $i, j$ entry is $a_{ji}$.
\end{definition}
The adjoint shows up on p. 122
Apostol uses ``column matrix'' and ``column vector'' synonymously: vol 1., p. 592 conflates the notions of tuple, array, vector and matrix (!):
We shall display the $m$-tuple $(t_{1k}, \dots, t_{mk})$ vertically... [t]his array is called a \textit{column vector} or a \textit{column matrix}.
If we interchange the rows and columns of a rectangular matrix $A$, the new matrix so obtained is called the \textit{transpose} of $A$ and is denoted by $A^t$. (p. 615, Exercise 7).
(Another axiom: $(A^t)^{-1} = (A^{-1))^t$)
