![]() ![]() One is not necessarily better than the other.Or M m × n ( R ). ![]() A more practical alternative, sometimes known as the Q-less QR factorization, is available. The unitary matrix Q often fails to have a high proportion of zero elements. Q,R,E qr (S) but this is often impractical. If you dont need C explicitly - like for iterative solvers - you can define an abstract linear operator that returns the vectorized product Cx. There are different traditions of teaching this stuff. MATLAB computes the complete QR factorization of a sparse matrix S with. The larger code performs such multiplications at multiple instances. F 1.B + 2.C + 3.D G 4.B + 5.C + 6.D H 7.B + 8. While doing that, I was surprised once again to find that Matlab is faster than C++ in matrix assembly and computation.I have a slightly larger code, from which I am investigating a segment of matrix-vector multiplication. What you should do as mentioned in the comments is to use the. If at least one input is scalar, then AB is. That is, AB is typically not equal to BA. Matrix multiplication is not universally commutative for nonscalar inputs. C (i,j) A (i,:)B (:,j) For nonscalar A and B, the number of columns of A must equal the number of rows of B. where I is the identity matrix, and the above are stacked vectors and matrix where all the rows and columns are appended together. You can write this definition using the MATLAB ® colon operator as. ![]() So it's not quite accurate to say that this is "not kosher". What you want to do is this giant sparse matrix multiplication. When I studied linear algebra, we started with vectors, not "row vectors" and "column vectors", and I didn't find it confusing. I believe most of these people come from MATLAB or MATLAB-inspired software which typically doesn't support vectors at all, only row and column matrices. This is all unnecessary complication in Mathematica, which does support proper 1D vectors, as well as N-D tensors. ![]() On Mathematica.SE I regularly see people trying to use "row vectors" and "column vectors" and a lot of transposision and complex indexing to try to do simple tasks. I find this implementation much more logical and consistent than what I see in rigidly matrix based systems like MATLAB, which don't even support vectors. Correspondingly, Dot does tensor contraction, not just matrix multiplication. Mathematica was designed to work with tensors of arbitrary dimensions, not just 2-dimensional matrices. But for beginners, I think it would be good not to have any extra quirks or hurdles for them to get over. I'm assuming that the different forms of bracketing needed in column vectors versus row vectors have some payoff later in terms of being able to use the Dot function with tensors. It is a good feature that I can use oblong matrices to put all my vertices into, so I won't complain too much about these small difficulties. If I have time, I'll try to develop a linear algebra package that lets me use the time-tested traditional notation, from square brackets, to a space meaning matrix multiplication, to always being able to use traditional matrix and vector layout. The iterative solvers require to determine the product Ax where x is the test solution. I use iterative solvers because the size of A is say 40000x40000. Even TraditionalForm, doesn't give the expected, traditional list of vectors in column form. I have to solve in MATLAB a linear system of equations AxB where A is symmetric and its elements depend on the difference of the indices: Aijf (i-j). But it would be much easier just to have Mathematica convert row and column vectors to lists when they're passed to ParametricPlot, etc.Īlso, couldn't matrices be threaded over lists of vectors, instead of requiring the clutter of mapping the dot-product?Īnd why doesn't MatrixForm applied to the result give me the expected list of matrices, in standard layout. I've figured out that I can just add in a substitution rule to do that, so I guess that's not too much to ask. One main wish: Anywhere we have what is a vector argument to a function, we should be able to type it as a row or column vector. ![]()
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