Matrix which is 1 when row and column are both odd or both even

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I want to create a matrix which which has:

  • The value 1 if the row is odd and the column is odd
  • The value 1 if the row is even and the column is even
  • The value 0 Otherwise.

I want to get the same results as the code below, but in a one line (command window) expression:

 N=8;
 A = zeros(N);

 for row = 1:1:length(A)
     for column = 1:1:length(A)
        if(mod(row,2) == 1 && mod(column,2) == 1)

             A(row,column*(mod(column,2) == 1)) = 1;

         elseif(mod(row,2)== 0 && mod(column,2) == 0 )

             A(row,column*(mod(column,2) == 0)) = 1;

        end
     end
  end
 disp(A)

This is the expected result:

 1     0     1     0     1     0     1     0
 0     1     0     1     0     1     0     1
 1     0     1     0     1     0     1     0
 0     1     0     1     0     1     0     1
 1     0     1     0     1     0     1     0
 0     1     0     1     0     1     0     1
 1     0     1     0     1     0     1     0
 0     1     0     1     0     1     0     1

A simple approach is to use implicit expansion of addition, noting that

odd+odd = even+even = 0

So this is your answer:

A = 1 - mod( (1:N) + (1:N).', 2 );

You could also do this with toeplitz, as shown in this MATLAB Answers Post

For a square matrix with number of rows = number of columns = N

A = toeplitz(mod(1:N,2));

If the number of rows (M) is not equal to the number of columns (N) then

A = toeplitz(mod(1:M,2),mod(1:N,2))

FWIW, you're asking a specific case of this question:

How to generate a customized checker board matrix as fast as possible?

m\times n$ matrix with an even number of 1s in each row and column, Hint: If m=1 or n=1, the problem is simple. So suppose they are both >1. Fill in everything with 0's and/or 1's except the bottom row and the� Multiplying a Row by a Column We'll start by showing you how to multiply a 1 × n matrix by an n × 1 matrix. The first is just a single row, and the second is a single column. By the rule above, the product is a 1 × 1 matrix; in other words, a single number. First, let's name the entries in the row r 1 , r 2 ,


Can you take three lines?

N=8;
A = zeros(N);
A(1:2:end, 1:2:end) = 1;
A(2:2:end, 2:2:end) = 1;

One line solution (when N is even):

A = repmat([1, 0; 0 1], [N/2, N/2]);

How to count matrices with rows and columns with an odd number of , For m>0, we have ∑k(−1)k(mk)=(1−1)m=0 and ∑k(mk)=(1+1)m=2m. So ∑k od d(mk)=(2m−0)/2=2m−1. Your identity is (2m−1)n−1=(2n−1)m−1. One way that some people remember that the notation for matrix dimensions is rows by columns (Rather than columns by rows) is by recalling a once popular-soda: RC Cola-- rows before columns! Below, you can see two pictures of the same matrix with the rows and columns highlighted. The dimensions of this matrix. dimensions: 2 × 3; 2 rows × 3


You can try the function meshgrid to generate mesh grids and use mod to determine even or odd

[x,y] = meshgrid(1:N,1:N);
A = mod(x+y+1,2);

such that

>> A
A =

   1   0   1   0   1   0   1   0
   0   1   0   1   0   1   0   1
   1   0   1   0   1   0   1   0
   0   1   0   1   0   1   0   1
   1   0   1   0   1   0   1   0
   0   1   0   1   0   1   0   1
   1   0   1   0   1   0   1   0
   0   1   0   1   0   1   0   1

How do I extract the odd and even rows of my matrix into two , Learn more about matrix, matrices, reorder, row, column, even, odd, reconstruct, for, loop, rearrange One contains the odd rows and another the even ones. Adding respectively an extra row or column to a table so that the parity of all columns or rows respectively is odd or even is always straightforward. Adding both at once adds one extra cell that is overspecified (at the intersection of extra column and row - at bottom right hand corner if we extend in length and to the right).


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