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Hey everyone.

I have been trying to solve an ODE with BC with dsolve,numeric but always get the error below:

> Error, (in dsolve/numeric/BVPSolve) matrix is singular

My problem is not solving it (ie fine to do with LinearAlgebra package or similar), but why does this error occur? What is the problem with the ODE/BC that produces this error?

And is there a way of adjusting the ODE/BC to be able to solve it simply by using dsolve,numeric?

One of the challenges in Linear Algebra is in developing problems, projects, and exercises that are both larger dimensional and student-accessible. Indeed, round-off error, computational complexity, difficulty factoring characteristic polynomials of degree 3 or higher, and similar aspects often mean that any problems or applications of rank 3 or higher are approached solely via technology. 

However, that same technology can be used to create...

I have come across this previously but I never had the energy to report it.
The problem is that there exist a bug in Vector[row] when n>10.

For example run the below code:

restart:
with(LinearAlgebra):
a1 := Vector[row]([seq(w[i], i = 1 .. 5)]);
a2 := Vector[column]([seq(w[i], i = 1 .. 5)]);

a3 := Vector[row]([seq(w[i], i = 1 .. 20)]);
a4 := Vector[column]([seq(w[i], i = 1 .. 20)]);

a1.a2;
a3.a4;

   ...

Does anyone happen to have a worksheet that implements LinearAlgebra[Generic][SmithForm] 

for Euclidean domains like Z[w], w^3 = 1, or Z[sqrt(d)] where d = −11, −7, −3, −2, −1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, 73?

If so I would greatly appreciate receiving a copy of it.

--Edwin Clark

I am using the LinearAlgebra package. The function SinbularValues returns the singular value matrix S as a vector, i.e.,S*<1,1,1..1>.  Is there an easy way to recover S, itself, from this vector?

I was going to demonstrate the action of Maple for a symmetric 3 by 3 real matrix with 1, 2, and 3 distinct eigenvalues and got strange results.  It may be that I need to explicitly tell Maple that the matrix is symmetric and real. (How would I do this?)

For example, after   with(LinearAlgebra)    I put   tmat1:=Matrix(3,3,[1,2,3,2,4,5,3,5,6]), and get eigenvalues with small imaginary parts (!).   When I put   tmat2:=Matrix(3,3,[0,1,1,1,0,1,1,1,0...

Answering to that question, I posted several procedures finding minimal polynomials for the elements of finite fields. The best one was the following,

alias(a=RootOf(T^100+T^97+T^96+T^93+T^91+T^89+T^87+T^86+T^82+T^81+T^71+T^70+T^67+T^61+
T^60+T^57+T^54+T^53+T^52+T^49+T^48+T^45+T^44+T^42+T^39+T^36+T^33+T^32+T^31+T^29+T^28+T^27+
T^26+T^24+T^23+T^22+T^18+T^17+T^16+T^14+T^13+T^12+T^10+T^8+T^7+T^6+T^3+T+1)):

F:=GF(2,100,op(a)):
z:=F:-input(2):

MinPolyGF:=proc(x,y:=_X)
local A, i;
A:=Matrix(100,...

I am computing eigenvalues of a 3X3 square Matrix that contains symbolic elements and many zeros. There are 2 zero eigenvalues and 1 non-zero. I'd like to request Maple to order the eigenvalues in a certain way, with the non-zero eigenvalue first. Oddly, the command LinearAlgebra:-Eigenvectors(A); orders them in a seemingly random way, with the non-zero eigenvalue either first or last, never in the middle. The LinearAlgebra:-Eigenvalues(A); commands seems...

Error, (in LinearAlgebra:-LA_Main:-MatrixInverse) singular matrix

what does this mean?

Hello all,

I have encountered a curious bug in the EigenConditionNumbers
procedure. In particular for a pencil pencil (A,B) with B singular,
and precision higher than hardware precision.

The following code for Digits=40 produces a Float(undefined) rather
than a Float(infinity) for the infinite eigenvalue, but an alpha and
beta that will produce an infinite eigenvalue.

Digits:=trunc(evalhf(Digits));
A:=Matrix([[1,0],[0,2]]);
B:=Matrix([[1,0],[0,0]]);

I have gotten some comments about my new avatar, including a few commenting that while my picture is clear on the blog contributors sidebar, it is "blurry" on my blog posts. I just wanted clear this up.  I am not in the witness protection program; I just really love singular values.  My new avatar, just like my old one, is a rank 4 approximation of a picture of me using the singular value decomposition.

 If you see my last question "use fsolve or matrix dissection"CCC.mw 

I want to find C, i finally solve it and get My special C

Now , I Want tolve My problem in block mode,
CCCd.mw

this means that, My matrix elemnts are block matrix, and search for result,

As alluded to in my previous post in this series, one of the most straight forward ways to test if a PRNG is generating good random sequences is by examining the frequency of 0's and 1's.  This is just a couple lines in Maple using Statistics:

(**) r1 := rand(0..1):L := [seq(r1(), i=1..10000)]:
(**) n := nops(L); tally := `+`(op(L));
(**) Statistics:-ChiSquareGoodnessOfFitTest(
      [n-tally, tally], [n/2, n/2], ':-output'=':-hypothesis');

 hi

I am new in LinearAlgebra and i have many question in it,

My problem is in this pdf files and i described in it my question.

Matrix.pdf

 hi

I want to solve this problem

Symbolic_Matrix.pdf  

with that code

sumbolic_matrix.mw