What is the correct NumPy representation of a row vector for gradients

Question

I am doing an assignment on matrices and gradients, where the final answer must be expressed as a row vector.

vr = np.array([1, 2, 3])
vrr = np.array([[1, 2, 3]])

Mathematically, a row vector should be a 1×3 matrix, so the shape (1,3) seems to match that idea. However, NumPy treats (3,) as a 1D array, and many operations, like dot products and gradients, seem to work with this form as well.

What I want to clarify:

Which of these is the true mathematical row vector?
Which one should I use when a question explicitly asks for a row vector gradient?
Is using shape (3,) mathematically ambiguous compared to (1,3)?

AztecCodes · Accepted Answer · 2025-11-26 18:09:21Z

3

Correct mathematical representation would be:

v = np.array([[1, 2, 3]]) # A (3,) NumPy array is not a matrix. It is a 1-dimensional object with no orientation at all.

Go for shape(1,n): This is the only form that is unambiguously a row vector.
Yes. The (3,) array has no row/column orientation. It can't be multiplied by matrices using true linear algebra rules unless NumPy broadcasts/coerces it.

answered Nov 26 at 18:09

AztecCodes

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