Vectorization with two dimensions at the same time

I have 2x10x10 matrix.

ans(:,:,1) =

     1     3     5     7     9    11    13    15    17    19
     2     4     6     8    10    12    14    16    18    20


ans(:,:,2) =

    21    23    25    27    29    31    33    35    37    39
    22    24    26    28    30    32    34    36    38    40

...
    
a(:,:,9) =

   161   163   165   167   169   171   173   175   177   179
   162   164   166   168   170   172   174   176   178   180


a(:,:,10) =

   181   183   185   187   189   191   193   195   197   199
   182   184   186   188   190   192   194   196   198   200
   

I want to erase the certain column of each 10 2D matries.

The rule is simple, on case of the first 2D matrix, erase first column. And second matrix, erase second column. Proceed diagonally.

If i implement this idea into for loop, it would be

for i=1:10
    a(:,i,i)= [];
end

As I checked, it doesn't work. MATLAB produces the error saying "a null assignment can have only one non-colon index".

If above code works, then result should be like 2x9x10 matrix.

ans(:,:,1) =

      3     5     7     9    11    13    15    17    19
      4     6     8    10    12    14    16    18    20


ans(:,:,2) =

    21    25    27    29    31    33    35    37    39
    22    26    28    30    32    34    36    38    40

...
    
a(:,:,9) =

   161   163   165   167   169   171   173   175   179
   162   164   166   168   170   172   174   176   180


a(:,:,10) =

   181   183   185   187   189   191   193   195   197
   182   184   186   188   190   192   194   196   198

After writing, It looks like there are two questions about it.

1. How can I assign null array by using two indices (`a(:,i,i)`)?
2. And how can I vectorize it?

In vectorization, I also tried the pythonic way, but it didn't work.

a(:, 1:10, 1:10) = [];  % a null assignment can have only one non-colon index

Answer 1

[Matt J]

How can I assign null array by using two indices (`a(:,i,i)`)?

You cannot. The way you would get what you're after here is as follows.

[m,n,p]=size(a);

a(:,1:n+1:end)=[];
a=reshape(a,m,[],p)

[Hwang Woosung]

Impressive.

Answer 2

[Matt J]

Here's a less efficient way, but one which generalizes more flexibly to other kinds of deletions you might want to do,

[m,n,p]=size(a);
[~,J,K]=ndgrid(1:m,1:n,1:p);

a(J==K)=[];

a=reshape(a,m,[],p);