Is matrix-vector product a dot or cross product 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.
 A: 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.
A: 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.
