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3
votes
2answers
133 views

Summing matrix products

I need to compute a double sum over a weighted matrix product: $L[M]=\sum_{i,j}^{N}\Lambda[[i]]\;\omega[[i]].M.\omega^{\dagger}[[j]]$. $\Lambda$ is a list of with N complex values(weights) and ...
5
votes
3answers
303 views

Bilinear Dot Function

In mathematics the matrix product is a bilinear operation $$ \alpha A \cdot(\beta B + \gamma C) = \alpha\beta ( A \cdot B )+ \alpha \gamma (A\cdot C ), $$ where capital letters denote matrices and ...
3
votes
0answers
115 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
1
vote
1answer
89 views

Using the Norm Function

I am trying to take the norm of a general vector and show that for vectors, v,w, that Norm[v cross w]^2==Norm[v]^2*Norm[w]^2-(v dot w)^2 In Mathematica, here are my steps: ...
1
vote
1answer
85 views

Pulling out a prefactor from a dot product

I have three complicated vectors u, v and w as well as three simple prefactors ...
4
votes
2answers
124 views

Factor out the scalar multiplier for the dot product of 2x2 matrices

If yy and zz are 2x2 Hermitian matrices, is there a way that I can mark them (with a property?) as Hermitian so that Mathematica can assume that it can factor out and simplify scalar multipliers from ...
1
vote
1answer
106 views

Unexpected inefficiency when calculating matrix product by Dot

There is an unexpected inefficiency when I calculate matrix product by Dot. The only relevant part of my code is presented as follows: ...
4
votes
2answers
168 views

Dot product for lists

Suppose we want to get the dot product for the following lists aa and bb, whose elements (a, ...
18
votes
3answers
699 views

Why is calling Dot with many arguments so inefficient?

Say I want to multiply a reasonably large list of symbolic matrices. ...
12
votes
1answer
296 views

Why does partitioning increase Dot execution speed?

I have noticed that multiplying a list of matrices can be significantly sped up by partitioning the list, calculating the product of the partitions matrices, and then multiplying the results. ...
3
votes
1answer
472 views

Draw grid with points

How would I draw a grid with dots on specified intersections? The image below shows the basic idea: If I wanted to label the grid lines with index numbers or letters, how would I do that?