If vectors are a special case of a matrix, then how is A transpose B ≡ A ∙ B (dot product)

inner-productsmatrices

If I have two vectors of equal dimensions like 3×1 lets say, how am I able to multiply it with another vector of 3×1 dimension? Its not possible in matrix operation.

Edit: Seems like most of you didn't get my question. If vectors ARE matrices and A and B has the same dimensions (3×1), it should not have been possible to multiply no?

Best Answer

The dot product of two vectors is defined as

$$\bar{v} . \bar{u} = v^Tu$$

This would result in a $1 \times 1$ real number

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