IMO, all this follows directly from pre-exisiting Julia choices 1 != (scalars and 1D vector spaces are distinct) and Vector != Matrix (operators and vectors are distinct). That is, we can multiply Mx1 matrices by 1xN matrices - which is fine and already exists, but it doesn't justify the method requested in the OP. And since Julia treats vectors and matrices as distinct, that implies that u must be a matrix. If we replace wᵀ with a linear operator from a N-dimensional vector space to a 1-dimensional vector space (remember Julia says a 1D vector space is distinct from a scalar) then that implies u is an operator from 1-dimensional vector space to an M-dimensional vector space. v) and we choose to write this linear map as A = u. Take again the last sentence in my notation description aboveĬomposing scalar-vector multiplication with the inner product means we can define a linear map that takes v and emits u.( wᵀ. A.' I feel this is associate one-dimensional vector spaces with scalars (in Julia, that is 1 = ). To me, it seems exceeding inelegant to add to the end of this mathematical notation description 'Oh, and by the way, in the special case that an operator A is a mapping from a 1-dimensional vector space to a n-dimensional vector space, we also allow you to write v. wᵀ.' In the universities I've been associated with, a good student at the end of first-year math should be comfortable with this (plus eigenvalues, inverses, etc). Composing scalar-vector multiplication with the inner product means we can define a linear map that takes v and emits u.( wᵀ.

The inner product induced by the duals (returning a scalar) is written vᵀ. To disentangle the argument, rather than consider Dirac notation, the corresponding mathematical notation I was aiming for would be this: 'Consider vectors v, w, etc and their duals vᵀ, wᵀ, etc, as well as linear operators A, B, etc. MATLAB always just called all of these arrays of numbers I would like to take a more (relatively elementary) abstract linear algebra approach. The point was never Dirac notation (which is definitely a confusing set of brackets for newcomers), but the appreciation of vectors, their duals and linear operators. Haha - that is quite a math lesson to learn from a short string. Since the *(A::AbstractVector, B::AbstractMatrix) method was an error if size(B, 1) was not 1, it is implied that the programmer knows for sure that B is a 1xN-shaped Array, which is guaranteed by B::RowVector. wᵀ and O = |psi> matlab mutiply vector by 3d matrix

A in an assignment/exam, and it would be a misuse of Dirac notation to write |psi> H and expect an operator back. You wouldn't impress a math lecturer with writing B = v. Otherwise vector * matrix doesn't make too much sense (outside of MATLAB/Householder notation, where matrices and vectors are of the same kind of object, which is just plain not true in Julia). In fact, this is still a (specialized) method of *(::AbstractVector, ::AbstractMatrix).

You can now do vector * rowvector for this. The (only) reason is it was a way of obtaining the outer product of two vectors. To me, the question is in reverse - why did this method exist in v0.5?

Matlab mutiply vector by 3d matrix