Largest elements in an array

Question

From the following page, there is this statement:

C = max(A,[],dim) returns the largest elements along the dimension of A specified by scalar dim. For example, max(A,[],1) produces the maximum values along the first dimension of A.

What do we mean by dimension here? Say that I have a matrix of size 30x2, what should I type in terms of the above to find the maximum element for each row?

Thanks.

Answer 1

As your name says, it is simple x)

The first dimension is the 30 in your example, the second 2. That is, the convention is as follows: 1st x 2nd x 3rd x 4th x nth dimension. We also call the 1st dimension as lines and the second as columns because that is how we are used to draw the matrices. I.e, suppose a matrix in matlab A, with dimensions nxm:

A =
           1st column  2nd column 3rd column …  mth column
1st line     A(1,1)      A(1,2)     A(1,3)   …    A(1,end)     
2nd line     A(2,1)      A(2,2)     A(2,3)   …    A(2,end)    
.              .           .          .      …      .
.              .           .          .      …      .
.              .           .          .      …      .
2nd line     A(end,1)    A(end,2)   A(end,3) …    A(end,end)

So using max on first dimension we find the max of all lines for each column, as follows:

max(A,[],1) =
           1st column  2nd column   3rd column  … mth column
1st line   max(A(:,1)) max(A(:,2))  max(A(:,3)) … max(A(:,end)) 

And the other case the maximum from all columns for each line:

max(A,[],2) =
             1st column
1st line     max(A(1,:))
2nd line     max(A(2,:))
.
. 
.
nthline      max(A(end,:))

This can be expanded into the next dimensions using the same logic.