How to add an NxN matrix with K pages ?

I have an NxN matrix with K pages where each element is a complex number. I need to add the corresponding elements in this K pages. How to do it?

For eg., if A is a 6 X 6 matrix with 4 pages, then I need to obtain solution for A(:,:,1) + A(:,:,2)+A(:,:,3) + A(:,:,4). Alternatively, I felt if using sum(), sum(A,4) should give my required answer. But sum(A,3) is giving the required answer. So, which command should be used to find the sum of elements in an NxN matrix having K pages?

Answer 1

[James Tursa]

You are correct, sum(A,3) is the correct syntax to use. This sums across the 3rd dimension.

[Syam MS]

What I need to obtain is sum of elements in all pages in the respective position in each page. How can i do that using sum() ? or is there any other alternate function for the same?

[James Tursa]

That is what sum(A,3) does. If A is a 6x6x4 array, sum(A,3) will be a 6x6 matrix where each element is the sum of that spot across the four pages. E.g., for a 3x3x4 array:

>> A = reshape(1:36,3,3,4)
A(:,:,1) =
     1     4     7
     2     5     8
     3     6     9
A(:,:,2) =
    10    13    16
    11    14    17
    12    15    18
A(:,:,3) =
    19    22    25
    20    23    26
    21    24    27
A(:,:,4) =
    28    31    34
    29    32    35
    30    33    36
>> sum(A,3)
ans =
    58    70    82
    62    74    86
    66    78    90
>> A(:,:,1) + A(:,:,2) + A(:,:,3) + A(:,:,4)
ans =
    58    70    82
    62    74    86
    66    78    90

This seems to be what you want. If it isn't, then I don't understand your real problem from your description.

[Syam MS]

That means if A is NxNxK array, always sum(A,3) need to be used. Thanks.

[James Tursa]

Yes. The sum(A,3) syntax works for any array sized NxNxK, and will sum all of the K pages since K is the 3rd dimension.