Items tagged with decomposition

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Q1: Pascal’s Matrix of order n is given by:
Sij =(i + j)!/ i!*j!
Use Mable to produce Pascal’s Matrix of order 8.

Q2: Study the Matrix decomposition (i.e. QR, LU, and LLT), then use Maple to produce these decompositions for a random Matrix of order 6.

Q3: Write one paragraph of your own to explain Moore-Penrose Inverse of a Matrix. Use Maple to find Moore-Penrose Inverse for a random Matrix of order 8.

Q4: Use Maple to find Jordan Canonical form for a random Matrix of order 10.

Q5: Use the seq command to generate the triple [i,j,k] for all possible values for 1 ≤ i,j,k ≤ 10, then plot this triple. i.e. Use nested seq .

Q6: Let F[n] be the set:
F[n] = {p / q: 1 ≤ q ≤ n,p ≤ p ≤ q}
Use Maple to find F[6].

I have a vector x of this type:

x :=Vector[column]([A__11*u__1+A__12*u__2+...+A__1m*u__m,

A__21*u__1+A__22*u__2+...+A__2m*u__m,

...,

A__n1*u__1+A__n2*u__2+...+A__nm*u__m]);

If I define u:=Vector[column]([u__1,u__2,...,u__m]), then it is clear that the equation has the form x=A*u.

I want to extract the matrix A, for the given vectors x and u.

IMPORTANT: I know I could create a loop (i=1 to m) and set u__i=1 and all other u__j=0 (for all j not equal i) and then reconstruct each column by this method, but it seems to be a overkill for such an easy problem.

I would be glad, if someone could show me a method how one can achive this in maple.

Has anyone been able to do multivariate partial fraction decomposition in maple (here is a paper introducing the idea https://arxiv.org/pdf/1206.4740.pdf)

I often find maple generating complicated rational functions that it would be nice to visualise in other ways

Here is an example of such a function if anyone wants to have a play:

 

(a*x^3+b*x*y^2+a*x*y+b*y^2)

/(a*x^3+a*b*x*y^2+a*b*y*x^2+b*y^3)

 

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