numpy.dot(a, b) gives wrong result on multiplication of matrices with similar dimenstions

Question

Let matrices a, b be [ 1, 2, 3, 4 ] ie of (1 x 4) dimension.
On applying numpy.dot(a, b) the result is 30 instead of raising exception that both the matrices shapes are not aligned.
How can a (mxn) matrix be multiplied with (mxn) matrix? Does numpy automatically transposes one matrix to align their shapes and then multiply?

Answer 1

In [59]: a = b = np.matrix([1,2,3,4])

In [60]: np.dot(a.T, b)      # 1
Out[60]: 
matrix([[ 1,  2,  3,  4],
        [ 2,  4,  6,  8],
        [ 3,  6,  9, 12],
        [ 4,  8, 12, 16]])

In [63]: np.dot(a, b.T)      # 2
Out[63]: matrix([[30]])

In [64]: np.dot(a, b)        # 3
ValueError: shapes (1,4) and (1,4) not aligned: 4 (dim 1) != 1 (dim 0)

More generally, if X has shape (m, n) and Y has shape (n, p) , then np.dot(X,Y) returns an array of shape (m, p) and which is the result of matrix multiplication.

1. Since aT has shape (4, 1) , and b has shape (1, 4) , the result of matrix multiplication is an array of shape (4, 4) .

2. Since a has shape (1, 4) , and bT has shape (4, 1) , the result of matrix multiplication is an array of shape (1, 1) .

3. np.dot(a, b) raises a ValueError since arrays of shape (1, 4) and (1, 4) can not be matrix multiplied. NumPy never transposes axes automatically.