The result that is returned for a particular expression is described below. In each of the following sections:

- A is an Array

- M is a Matrix

- V is a Vector

- c is a numeric constant

- s is a non-numeric scalar

The result that is returned when an expression of type '+' includes at least one rtable depends on the operands.

Direct evaluation of these expressions is implemented by calls to the rtable/Sum library routine.

The result that is returned when an expression of type '*' includes at least one rtable depends on the operands. If the operands are either Matrices, Vectors, or a combination of each (with appropriate dimensions), the '.' operator must be used. The . operator performs noncommutative or dot product multiplcation. For more information, see dot.

Direct evaluation of these expressions is implemented by calls to the rtable/Product library routine.

The result that is returned when an expression of type '^' includes an rtable object base depends on the exponent type.

There are two cases in which the exponent is interpreted specially: $R^{+}=\mathrm{LinearAlgebra}:-\mathrm{Transpose}\left(R\right)$ and $R^{*}=\mathrm{LinearAlgebra}:-\mathrm{HermitianTranspose}\left(R\right)$.  (The deprecated notations, $R^T$ and $R^H$, respectively, are similarly interpreted.)

Otherwise, the following interpretations of a power of an rtable apply.

Direct evaluation of these expressions is implemented by calls to the rtable/Power library routine.

$c≔2$

$c≔2$

$\mathrm{A1}≔\mathrm{Array}\left(\left[\left[1\,2\right]\,\left[3\,4\right]\right]\right)$

$\mathrm{A1}≔\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

$\mathrm{A2}≔\mathrm{Array}\left(\left[\left[u\,v\right]\,\left[w\,x\right]\right]\right)$

$\mathrm{A2}≔\left[\begin{array}{cc}u& v\\ w& x\end{array}\right]$

$\mathrm{M1}≔⟨⟨1\,2⟩|⟨-2\,1⟩⟩$

$\mathrm{M1}≔\left[\begin{array}{cc}1& \mathrm{-2}\\ 2& 1\end{array}\right]$

$\mathrm{M2}≔⟨⟨2\,3⟩|⟨4\,4⟩⟩$

$\mathrm{M2}≔\left[\begin{array}{cc}2& 4\\ 3& 4\end{array}\right]$

$\mathrm{V1}≔⟨x|y⟩$

$\mathrm{V1}≔\left[\begin{array}{cc}x& y\end{array}\right]$

$\mathrm{A1}+\mathrm{A2}$

$\left[\begin{array}{cc}1+u& 2+v\\ 3+w& 4+x\end{array}\right]$

$\mathrm{A1}+c$

$\left[\begin{array}{cc}3& 4\\ 5& 6\end{array}\right]$

$\mathrm{A1}+s$

$s+\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

$\mathrm{M1}+\mathrm{M2}$

$\left[\begin{array}{cc}3& 2\\ 5& 5\end{array}\right]$

$\mathrm{M1}+c$

$\left[\begin{array}{cc}3& \mathrm{-2}\\ 2& 3\end{array}\right]$

$\mathrm{M1}+s$

$s+\left[\begin{array}{cc}1& \mathrm{-2}\\ 2& 1\end{array}\right]$

$\mathrm{A1}\mathrm{A2}$

$\left[\begin{array}{cc}u& 2v\\ 3w& 4x\end{array}\right]$

$\mathrm{A1}·\mathrm{A2}$

$\left[\begin{array}{cc}u& 2v\\ 3w& 4x\end{array}\right]$

M1 * M2;

Error, (in `rtable/Product`) use *~ for elementwise multiplication of Vectors or Matrices; use . (dot) for Vector/Matrix multiplication

$c\mathrm{M1}$

$\left[\begin{array}{cc}2& \mathrm{-4}\\ 4& 2\end{array}\right]$

$c·\mathrm{M1}$

$\left[\begin{array}{cc}2& \mathrm{-4}\\ 4& 2\end{array}\right]$

$s\mathrm{M1}$

$\left[\begin{array}{cc}s& -2s\\ 2s& s\end{array}\right]$

$s·\mathrm{M1}$

$s·\left[\begin{array}{cc}1& \mathrm{-2}\\ 2& 1\end{array}\right]$

$\mathrm{M1}·\mathrm{M2}$

$\left[\begin{array}{cc}\mathrm{-4}& \mathrm{-4}\\ 7& 12\end{array}\right]$

$\mathrm{V1}·\mathrm{M2}$

$\left[\begin{array}{cc}2x+3y& 4x+4y\end{array}\right]$

${\mathrm{A1}}^c$

$\left[\begin{array}{cc}1& 4\\ 9& 16\end{array}\right]$

${\mathrm{A1}}^s$

$\left[\begin{array}{cc}1& 2^s\\ 3^s& 4^s\end{array}\right]$

${\mathrm{M2}}^c$

$\left[\begin{array}{cc}16& 24\\ 18& 28\end{array}\right]$

${\mathrm{M2}}^s$

${\left[\begin{array}{cc}2& 4\\ 3& 4\end{array}\right]}^s$

${\mathrm{M2}}^{\mathrm{\%T}}$

$\left[\begin{array}{cc}2& 3\\ 4& 4\end{array}\right]$

${\mathrm{V1}}^{\mathrm{\%H}}$

$\left[\begin{array}{c}\stackrel{\&conjugate0;}{x}\\ \stackrel{\&conjugate0;}{y}\end{array}\right]$