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3 x 4 matrix as vector

I want to find out if a matrix M is a vector.

A matrix has a few properties:

it's a square matrix (a M x M matrix),

it's symmetric,

and it's the Cartesian product of two vectors.

For example, M = [[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1], [1, 1, 1, 0]] is a vector, as it can be written as:

M = [1, 1, 0, 0]

[1, 0, 1, 0]

[1, 0, 0, 1]

[1, 1, 1, 0]

In general, I want to write a boolean function to check if a matrix is a vector.

I know how to find out if a matrix is symmetric, and how to find out if it's a vector, as a vector is symmetric.

Therefore, my question is: How can I check if a matrix is the Cartesian product of two vectors?

In the example above, it's the case.

Construct a matrix from the input, call it M'.

Then, construct a similar matrix M'', for which the input is N^2 vectors, where N is the size of the input matrix.

Finally, convert M' and M'' to M form.

Result is:

M is a vector iff M'' is the same as M'.

Here's code in python:

def isVector(M):

M = np.asarray(M)

N = M.shape[0]

if M.shape[0]!= N**2:

print('input matrix must be square')

else:

for i in range(N):

if M[i,i]!= M[i,i]:

print('all elements 0b46394aab

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