$v:=⟨3\,2\,1⟩$

$v:=\left[\begin{array}{r}3\\ 2\\ 1\end{array}\right]$

$w:=⟨a\|b\|c⟩$

$w:=\left[\begin{array}{ccc}a& b& c\end{array}\right]$

$A≔⟨⟨1\,2\,3⟩\|⟨4\,5\,6⟩⟩$

$A:=\left[\begin{array}{rr}1& 4\\ 2& 5\\ 3& 6\end{array}\right]$

$B:=⟨⟨a\|b\|c⟩\,⟨d\|e\|f⟩⟩$

$B:=\left[\begin{array}{ccc}a& b& c\\ d& e& f\end{array}\right]$

$C:=⟨v\|⟨4\,5\,6⟩⟩$

$C:=\left[\begin{array}{rr}3& 4\\ 2& 5\\ 1& 6\end{array}\right]$

$B:=⟨w\,w⟩$

$B:=\left[\begin{array}{ccc}a& b& c\\ a& b& c\end{array}\right]$

$⟨A\|⟨x\,y\,z⟩⟩$

$\left[\begin{array}{ccc}1& 4& x\\ 2& 5& y\\ 3& 6& z\end{array}\right]$

$\mathrm{type}\left(v\,\mathrm{Vector}\right)$

$\mathrm{true}$

$\mathrm{type}\left(A\,\mathrm{Matrix}\right)$

$\mathrm{true}$

$\mathrm{type}\left(v\,\mathrm{vector}\right)$

$\mathrm{false}$

$\mathrm{type}\left(B\,\mathrm{matrix}\right)$

$\mathrm{false}$

$B\.A$

$\left[\begin{array}{cc}a\+2b\+3c& 4a\+5b\+6c\\ a\+2b\+3c& 4a\+5b\+6c\end{array}\right]$

$w\.A$

$\left[\begin{array}{cc}a\+2b\+3c& 4a\+5b\+6c\end{array}\right]$

$A\+⟨⟨a\,b\,c⟩\|⟨d\,e\,f⟩⟩$

$\left[\begin{array}{cc}1\+a& 4\+d\\ 2\+b& 5\+e\\ 3\+c& 6\+f\end{array}\right]$

$w\.w$

$a^2\+b^2\+c^2$

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

$\left[\begin{array}{cc}a& a\\ b& b\\ c& c\end{array}\right]$

$A^{\mathrm{\%T}}\.v$

$\left[\begin{array}{r}10\\ 28\end{array}\right]$

${⟨1\+I\,2I⟩}^{\mathrm{\%H}}$

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

$⟨1\,2\,3⟩ \&x ⟨a\,b\,c⟩$

$\left[\begin{array}{c}2c-3b\\ 3a-c\\ b-2a\end{array}\right]$

Most commands in the Student[LinearAlgebra] subpackage consider symbolic quantities to represent real variables. For example, a dot product of Vectors whose entries are symbolic expressions does not use complex conjugates when computing the result. This assumption is specific to the Student[LinearAlgebra] subpackage and does not hold in the main LinearAlgebra package. To allow variables to represent complex-valued quantities, use the package command, SetDefault( conjugate = true ).

All syntaxes, except for the cross product (&x), are available throughout Maple, whether or not the Student[LinearAlgebra] subpackage has been loaded. The definition of the . (dot) operator is, however, different if the Student[LinearAlgebra] subpackage has been loaded, in that it then treats symbolic quantities as being real-valued by default, as discussed earlier.

$\mathrm{Id}\left(2\right)$

$\left[\begin{array}{rr}1& 0\\ 0& 1\end{array}\right]$

$\mathrm{RandomMatrix}\left(4\right)$

$\left[\begin{array}{rrrr}-93& -32& 8& 44\\ -76& -74& 69& 92\\ -72& -4& 99& -31\\ -2& 27& 29& 67\end{array}\right]$

$\mathrm{DiagonalMatrix}\left(v\right)$

$\left[\begin{array}{rrr}3& 0& 0\\ 0& 2& 0\\ 0& 0& 1\end{array}\right]$

$\mathrm{JordanBlockMatrix}\left(\left[\left[{\mathrm{\λ}}_1\,3\right]\,\left[{\mathrm{\λ}}_2\,2\right]\right]\right)$

$\left[\begin{array}{ccccc}{\mathrm{\λ}}_1& 1& 0& 0& 0\\ 0& {\mathrm{\λ}}_1& 1& 0& 0\\ 0& 0& {\mathrm{\λ}}_1& 0& 0\\ 0& 0& 0& {\mathrm{\λ}}_2& 1\\ 0& 0& 0& 0& {\mathrm{\λ}}_2\end{array}\right]$

$\mathrm{UnitVector}\left[\mathrm{row}\right]\left(2\,5\right)$

$\left[\begin{array}{ccccc}0& 1& 0& 0& 0\end{array}\right]$

$\mathrm{CharacteristicMatrix}\left(⟨⟨1\,2\,3⟩\|⟨4\,5\,6⟩\|⟨7\,8\,9⟩⟩\,t\right)$

$\left[\begin{array}{ccc}t-1& -4& -7\\ -2& t-5& -8\\ -3& -6& t-9\end{array}\right]$

$\mathrm{RotationMatrix}\left(\frac{\mathrm{\π}}{6}\right)$

$\left[\begin{array}{cc}\frac{1}{2}\sqrt{3}& -\frac{1}{2}\\ \frac{1}{2}& \frac{1}{2}\sqrt{3}\end{array}\right]$

$B:=⟨⟨1\,2\,3⟩\|⟨4\,5\,6⟩\|⟨7\,8\,9⟩⟩$

$B:=\left[\begin{array}{rrr}1& 4& 7\\ 2& 5& 8\\ 3& 6& 9\end{array}\right]$

$\mathrm{ColumnDimension}\left(B\right)\,\mathrm{RowDimension}\left(B\right)\,\mathrm{Rank}\left(B\right)$

$3\,3\,2$

$\mathrm{Dimension}\left(B\right)\;$$\mathrm{Dimension}\left(v\right)$

$3\,3$

$3$

$\mathrm{IsDefinite}\left(⟨⟨3\,1\,1⟩\|⟨2\,4\,2⟩\|⟨1\,2\,5⟩⟩\right)$

$\mathrm{true}$

$\mathrm{IsOrthogonal}\left(⟨⟨3\,1\,1⟩\|⟨2\,4\,2⟩\|⟨1\,2\,5⟩⟩\right)$

$\mathrm{false}$