Going through linear algebra tutorials on khanacademy I've found that matrix-vector products are not defined clearly as dot or cross products. Am I missing something? Is matrix-vector product a dot or cross product?
At first I thought it's a cross product, because result is a vector, not a scalar. But cross-product is not defined in R2, however, matrix-vector product is allowed in R2. A bit confused.
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$\begingroup$Dot-products and cross-products are products between two like things, that is: a vector, and another vector. In a matrix-vector product, the matrix and vectors are two very different things. So, a matrix-vector product cannot rightly be called either a dot-product or a cross-product.
That being said, the matrix-vector product is closely related to the dot product. In particular: suppose that $A$ is a matrix with row-vectors $A_1,\dots,A_n$, and $b$ is a column vector. Then the product $Ab$ will be the column vector with entries $(A_1 \cdot b,\cdots,A_n \cdot b)$.
Moreover: given two column vectors $u$ and $v$, their dot-product is the same as the matrix product $u^Tv$, where $T$ here means the transpose. In this sense, we might consider the dot-product to be a kind of matrix product, but the reverse is not generally true.
$\endgroup$ 2 $\begingroup$I think what you refer to is row matrix times column matrix ,if so then you have 1 by n matrix (vector) times n by 1 matrix(vector) witch will give you a scalar; the same way as doing the dot product between two vectors. Important to remember that it has to be row vector * column . In that case you can think about it as a dot product,and you can apply the same idea in general matrices by multiplying row i with column j . I hope this is clear.
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