Linear Algebra with Applications, 10th Edition

Matrix Arithmetic

Addition and Multiplication of Matrices

Matrix arithmetic in MATLAB is straightforward. We can multiply our original matrix A times B simply by typing $A*B$. The sum and difference of A and B are given by $A+B$ and $A-B$, respectively. The transpose of the real matrix A is given by A′. For a matrix C with complex entries, the′ operation corresponds to conjugate transpose. Thus, $C^H$ is given as $C^{\prime }$ in MATLAB.

Backslash or Matrix Left Division

If W is an $n\times n$ matrix and b represents a vector in $R^n$, the solution of the system $W\mathbf{x}=\mathbf{b}$ can be computed using MATLAB’s backslash operator by setting

$$\mathbf{x}=\mathit{W}\backslash \mathbf{b}$$

For example, if we set

$$W=\left[\begin{array}{cccccccccccccccc}1& 1& 1& 1;& 1& 2& 3& 4;& 3& 4& 6& 2;& 2& 7& 10& 5\end{array}\right]$$

and $\mathbf{b}=\left[\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}3;& 5;\end{array}& 5;\end{array}& 8\end{array}\right]$, then the command

$$\mathbf{x}=\mathit{W}\mathbf{\backslash }\mathbf{b}$$

will yield

$$\begin{array}{c}\hfill \mathbf{x}=\\ \hfill 1.0000\\ \hfill 3.0000\\ \hfill -2.0000\\ \hfill 1.0000\end{array}$$

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