Linear Algebra with Applications, 10th Edition

Columnwise Array Operators

MATLAB has a number of functions that, when applied to either a row or column vector x, return a single number. For example, the command max(x) will compute the maximum entry of x, and the command sum(x) will return the value of the sum of the entries of x. Other functions of this form are min, prod, mean, all, and any. When used with a matrix argument, these functions are applied to each column vector and the results are returned as a row vector. For example, if

$$\begin{array}{cc}A& =\left[\begin{array}{cccc}\hfill -3& 2& 5& 4\\ \hfill 1& 3& 8& 0\\ \hfill -6& 3& 1& 3\end{array}\right]\end{array}$$

then

$$\begin{array}{cc}\hfill \mathsf{\text{min}}\left(A\right)& =\left(-6,2,1,0\right)\hfill \\ \hfill \mathsf{\text{max}}\left(A\right)& =\left(1,3,8,4\right)\hfill \\ \hfill \mathsf{\text{sum}}\left(A\right)& =\left(-8,8,14,7\right)\hfill \\ \hfill \mathsf{\text{prod}}\left(A\right)& =\left(18,18,40,0\right)\hfill \end{array}$$