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Anyone can help me with the problem ?

I want to solve b1..b50

> restart; with(plots); with(LinearAlgebra); with(Statistics);
> m0 := proc (t) options operator, arrow; 1-exp((-1)*t*.5) end proc;
t -> 1 - exp((-1) t 0.5)
> m := proc (t) options operator, arrow; (1/(1+exp(-t+5))-0.67e-2)*1.0067 end proc;
/ 1 \
t -> |--------------- - 0.0067| 1.0067
\1 + exp(-t + 5) /
> n[max] := 10; delt := .2; n := n[max]/delt;
> T := Vector(50);
> b := vector(50); evalm(b);

> for i from 2 to n do T[i] := T[i-1]+delt end do;
> fun := proc (t) options operator, arrow; add(b[i]*m0(t-T[i]), i = 1 .. n) end proc;
> fun(t);
> fu := vector(50);

> for x to 49 do fu[x] := fun(x*delt) = m(x*delt) end do;
> s := solve({fu[1 .. 50]}, {b[1 .. 50]});





ProjOfEigenVector := MatrixMatrixMultiply(BeProjected, (Transpose(OrthoBasis).MatrixInverse(MatrixMatrixMultiply(OrthoBasis, Transpose(OrthoBasis)), method = pseudo).OrthoBasis));

i use definition of this 

# P=(A*B’).inv(B*B’).B


however, no matter whatever matrix A pass into this equation in order to project onto B,

it still return the original matrix A

how can this definition be used to project a matrix onto another matrix?

how to correctly to project a matrix onto another matrix

how to decompose a matrix into time invariant and time variant 

is it possible to make time invariant and time variant template and then decompose into it


i mean decomposition can be 

 time invariant matrix + time variant matrix


 time invariant matrix * time variant matrix

 dsolve([Diff(f, t) = f, Diff(f,t) + g = h], f);

 dsolve([Diff(f, t) = f, Diff(f,t)*g = h], f);

where h is orthogonal matrix, f,g,h are matrix

would like to find g and f from h


can dsolve solve differential equation of matrix ? how?


dsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);


assume x^2 + 1 is from interpolation of polynomial

pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t)= x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);
pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t) = x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);

these system can not be solved


hope no real number any more after decomposition and only have iinteger in I time invariant function

if kernel is solve(A*x, x);

then , what is cokernel of a numeric matrix ?

how to solve this case which like sylvester

NullSpace(A*X+X*A) = B

find X?

 any things like 

A*X + X*A = NullSpace^-1(B)


if i assume Matrix([[x1,x2,x3],[x4,x5,x6],[x7,x8,x9]]);

find NullSpace(Matrix([[x1,x2,x3],[x4,x5,x6],[x7,x8,x9]]))

then from the equation of it, put all equations = 0, and then solve them

and then substitue value of B into the result, can it be said NullSpace^-1(B)?

a = c1*b + c2*c;
b = c3*a + c4*c;

where a, b, c are vector, a is linear combination of b and c, b is linear combination of a and c, and c1^2 + c2^2 = 1, c3^2 + c4^2 = 1

assume equation for a = c1*b + c2*c; is
Matrix([[y1],[y2]]) = Matrix([[x1,x2],[x3,x4]])*Matrix([[c1],[c2]]);

how to find c1 and c2 when c1^2 + c2^2 = 1


nothing return after solve({y1 = c1*x1 + c2*x2, y2 = c1*x3 + c2*x4, c1^2 + c2^2 = 1}, {c1,c2});

my question may be simple but I don't find the answer in any help guide.
when I define a function I cannot use a linearalgebra expression such as Trace.
Here is an example of what I would like to do:

If anyone can help me...
Thank you

I have following expression


which is 1 solution of the ODE

ode2 := -(diff(y(t), t, t))+(4-12/(1+s*cosh(2*t))+(8*(-s^2+1))/(1+s*cosh(2*t))^2)*y(t) = 0

Now I wanted to construct 2 linear independent solutions via:



and calculate the Wronskian:

with(LinearAlgebra); with(VectorCalculus)

Determinant(Wronskian([f(t_b-t), f(t-t_a)], t))

Since I know these functions are solutions of the second order ODE which does not contain any first order derivative the Wronskian should be a constant. Unfortunately Maple has a hard time to simplify it since the epxression is a little big. Is it my fault or has anyone an idea what to do?

I am using the ColumnSpace command (from the LinearAlgebra package) to generate a basis for the column space of a matrix. Is there any way to "force" the command to express the basis in terms of columns of A and not in the canonical form with leading 1's?

For example, for


I would like to obtain the following basis for the column space:



I've been playing around with the Basis command in the LinearAlgebra package. It's very easy to get a Basis for any subspace of R^n. However, if you're dealing with finite-dimensional polynomial or matrix spaces, the Basis command doesn't work. Due to some basic isomorphism theorems, we can always associate these vectors with those in R^n. I was wondering if there is a way to get Maple, via the Basis command, to handle "other types" of vectors. For example, how might one get Maple to return a basis of {x^2+x+4,x+3,2x^2-x-5,5x^2+x-7} in P_2, the space of polynomials of degree less than or equal to 2, or, a basis for {[[2,3],[5,6]],[[3,2],[0,1]],[[1,1],[0,5]]} in M_{2,2}, the space of 2 x 2 matrices, without converting to R^n?

How do you define funtion y"+2y'=0 y(0)=1.solve this question using in maple command!

I'm really struggling to do some linear algebra over Galois fields in Maple with LinearAlgebra package. I looked at the documentation for LinearAlgebra[Nodular] and LinearAlgebra[Generic], but i failed to get even simple examples to work. For instance as simple example over GF(2) I tried the following code which in my understanding should return the vector [1,1,1], instead this however simply no result seemt to be computed:



I have currently encountered a problem that I am not sure if is a mathematical problem or a problem with Maple itself. I want to find the eigenvalues and eigenvectors of the following matrix:

[[2.460*10^9*sin(theta)^2+8.970*10^6*cos(theta)^2, 0, 2.449*10^9*sin(theta)*cos(theta)], [0,8.450*10^6*sin(theta)^2+8.970*10^6*cos(theta)^2,0],[2.449*10^9*sin(theta)*cos(theta),8.970*10^6*sin(theta)^2+2.530*10^9*cos(theta)^2]]

Maple is able to conjure...

CAb := <1, 1, 2;1, 2, 3;1, 3, 1>;
# Get the QR decomposition of CAb:
Q, R := QRDecomposition(CAb); R;

Error in R

Maple Matrix(3, 3, {(1, 1) = 1.7321, (1, 2) = 3.4642, (1, 3) = 3.4642, (2, 1) = 0., (2, 2) = 1.4142, (2, 3) = -.70710, (3, 1) = 0., (3, 2) = 0., (3, 3) = 1.2248})

MathCad Matrix(3, 3, {(1, 1) = 1.7321, (1, 2) = 3.4642, (1, 3) = 3.4642, (2, 1) = 0., (2, 2) = 1.4142, (2, 3) =...

I have a large symmetric square 15x15 matrix (say B). With all entries in the region 0.285746383 and I am trying to calculate the eigenvalues of them using


B was originally an array that I converted to a Matrix with convert(B,Matrix).
I have also used type(B,Matrix) which returns true.

Yet when I enter Eigenvalues(B); It returns "Error, invalid input: LinearAlgebra:-Eigenvalues uses a 1st argument, A, which is missing"

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