Matrix/Vector Sampling

[jolyonb]

We would like to be able to say that A is a matrix of a given size, and sample appropriately. Alternatively, vecv is a vector of a certain size. Students can then input vector math expressions.

• Error should be raised when objects don't line up appropriately.
• We should decide how multiplication works. Is a vector times a vector a dot product?
• The identity matrix will need to be treated carefully.
• Row vs column vectors will need to be decided upon.
• We will probably need to make a transpose operation available, preferably as A^T. If a transposition operation is available, then vectors can be defined as a row/column vector and all multiplications work appropriately (dot products become v^T * v, for example).
• Special matrix samplers can be constructed (symmetric, antisymmetic, orthogonal, traceless, etc).
• Do we want to define a Hermitian conjugate operation? A^dagger?

[ChristopherChudzicki]

I'll have PR for this one tomorrow.

[jolyonb]

Awesome! I'm honestly surprised at how fast all of this has come together...

[jolyonb]

We should probably expand the equality grader to first check to make sure that the input has the same dimensions as the answer!

[jolyonb]

I'm going to go ahead and close this too. The only bit here that hasn't been implemented/superseded is a number of specialty matrix samplers, but that deserves its own issue. I seem to recall that the equality comparer checks for shape match as its first order of business; correct me if I'm wrong.