3 ms·
> inner product of a matrix and a vector how does that work?
by return0 12y ago
> inner product of a matrix and a vector
how does that work?
- fnbr 12y agoI think he just means the normal matrix product Av (where A is a n x m dimensional matrix and v a n dimensional vector). Wikipedia covers matrix multiplication in depth: http://en.wikipedia.org/wiki/Matrix_multiplication http://en.wikipedia.org/wiki/Matrix_multiplication
- RaptorJ 12y agoThe inner product in the context of tensors is a rank-contraction operation[0]. The IP you know and love contracts over the covariant and contravariant indicies of two rank-1 tensors (vectors). You need a metric to do this so you can raise one of the contravariant indicies to be covariant. If your metric is the normal one (all 1's) then you just add the product of all coefficients. Though if you have the Minkowski metric (like in special relativty) then you negate the time coordinate (or all the space coordinates) and add. Here the matrix might be regarded as a rank 1,1 tensor (one covariant, one contravariant index) that you contract with the vector. [0] http://en.wikipedia.org/wiki/Tensor_contraction http://en.wikipedia.org/wiki/Tensor_contraction