How to select a submatrix (not in any particular pattern) in Matlab

TLDR: Short Answer

As for your question, suppose you have an arbitrary 10-by-10 matrix A. The simplest way to extract the desired sub-matrix would be with an index vector:

B = A([1 2 9], [4 6]);

Indexing in MATLAB

There’s an interesting article in the official documentation that comprehensively explains indexing in MATLAB.
Basically, there are several ways to extract a subset of values, I’ll summarize them for you:

1. Indexing Vectors

Indexing vectors indicate the indices of the element to be extracted. They can either contain a single index or several, like so:

A = [10 20 30 40 50 60 70 80 90]

%# Extracts the third and the ninth element
B = A([3 9])  %# B = [30 90]

Indexing vectors can be specified for each dimension separately, for instance:

A = [10 20 30; 40 50 60; 70 80 90];

%# Extract the first and third rows, and the first and second columns
B = A([1 3], [1 2])  %# B = [10 30; 40 60]

There are also two special subscripts: end and the colon (:):

• end simply indicates the last index in that dimension.
• The colon is just a short-hand notation for “1:end”.

For example, instead of writing A([1 2 3], [2 3]), you can write A(:, 2:end). This is especially useful for large matrices.

2. Linear Indexing

Linear indexing treats any matrix as if it were a column vector by concatenating the columns into one column vector and assigning indices to the elements respectively. For instance, we have:

A = [10 20 30; 40 50 60; 70 80 90];

and we want to compute b = A(2). The equivalent column vector is:

A = [10;
     40;
     70;
     20;
     50;
     80;
     30;
     60;
     90]

and thus b equals 40.

The special colon and end subscripts are also allowed, of course. For that reason, A(:) converts any matrix A into a column vector.

Linear indexing with matrix subscripts:
It is also possible to use another matrix for linear indexing. The subscript matrix is simply converted into a column vector, and used for linear indexing. The resulting matrix is, however always of the same dimensions as the subscript matrix.
For instance, if I = [1 3; 1 2], then A(I) is the same as writing reshape(A(I(:)), size(I)).

Converting from matrix subscripts to linear indices and vice versa:
For that you have sub2ind and ind2sub, respectively. For example, if you want to convert the subscripts [1, 3] in matrix A (corresponding to element 30) into a linear index, you can write sub2ind(size(A), 1, 3) (the result in this case should be 7, of course).

3. Logical Indexing

In logical indexing the subscripts are binary, where a logical 1 indicates that the corresponding element is selected, and 0 means it is not. The subscript vector must be either of the same dimensions as the original matrix or a vector with the same number of elements. For instance, if we have:

A = [10 20 30; 40 50 60; 70 80 90];

and we want to extract A([1 3], [1 2]) using logical indexing, we can do either this:

Ir = logical([1 1 0]);
Ic = logical([1 0 1]);
B = A(Ir, Ic)

or this:

I = logical([1 0 1; 1 0 1; 0 0 0]);
B = A(I)

or this:

I = logical([1 1 0 0 0 0 1 1 0]);
B = A(I)

Note that in the latter two cases is a one-dimensional vector, and should be reshaped back into a matrix if necessary (for example, using reshape).