Items tagged with determinant

For exaqmple, the quadratic equation w^2 + uw + v = 0 corresponds to the deter minant


| -u  1  1  |

| v    0  1  |  = 0

|w^2 w w-1|

Is there any way to find a determinant corresponding to an equation, as above?

This is an issue in the preparation of a nomograph for the initial equation.  

It is generally solved by trial and error.

When I use the Determinant function on a matrix with (single variable) polynomial entries with real coefficients I often get an incorrect answer. I know the answers are incorrect because they have a higher degree or a lower lowest degree than is possible given the matrix elements.

However, when I replace the coefficients in the polynomials with rational numbers or I put in the option method=minor, I get the correct answer.

The problem seems to be roundoff error. However, the important error is not simply small changes in the resulting polynomial. The important error is the presence of entirely incorrect powers of the variable and not with very small coefficients.

How does this happen and why does the help page for Determinant( ) not warn of this behavior? In particuiar, why does the help page not say that using Gaussian elimination (i.e., the default) will often give incorrect answers in such cases, but using method=minor will work? Is this behavior known? I cannot find any reference to it on the internet.

hi....how i can extract Coefficients  (i.e. {f1[2],f2[2],f2[3],f3[2],.....f3[6]}) from every algebric equations and create matrix A ,in form AX=0, (X are f1[2],f2[2],f2[3],f3[2],.....f3[6] ) then the determinant of the matrix of coefficients (A) set to zero for obtaining unknown parameter omega.?

Note that  if m=3 then 6 equations is appeare and if m=4 then 9 equations is appeare.thus i need a procedure that works for every arbitary value of ''m''.

in attached file below m=4 thus we have 9 equations, i.e. 3 for eq1[k_] and 3 for eq2[k_] and so on...

also we should use boundary conditions for some amount of fi[j] (i=1,2,3 and j=2,3,...,7)

be extacting above Coefficients for example from first equation ,

''**:= (1/128)*f1[2]*omega^2-(1/4)*f2[2]-(1/2)*f2[3]+(1/4)*f2[4]+(1/4)*f3[2]-(1/2)*f3[3]+(1/4)*f3[4]+140*f1[2]-80*f1[3]+20*f1[4]'''

must compute

coeff(**, f1[2]); coeff(**, f2[2]) and so on...

 

 

 

 

 

fdm-maple.mw

 

 ############################Define some parameters

 

 
restart; Digits := 15; A1 := 10; A2 := 10; A3 := 10; A4 := 1; A5 := 1; A6 := 1; A7 := 1; A8 := 1; A9 := 1; A10 := 1; A11 := 1; B1 := 10; B2 := 10; B3 := 10; B4 := 1; B5 := 1; B6 := 1; B7 := 1; B8 := 1; B9 := 1; B10 := 1; B11 := 1; C1 := 10; C2 := 10; C3 := 10; C4 := 1; C5 := 1; C6 := 1; C7 := 1; C8 := 1; C9 := 1; C10 := 1; C11 := 1; C12 := 1; C13 := 1; C14 := 1; C15 := 1; C16 := 1; A12 := 1; B12 := 1; C18 := 1; C17 := 1; C19 := 1; n := 1; U := proc (x, theta) options operator, arrow; f1(x)*cos(n*theta) end proc; V := proc (x, theta) options operator, arrow; f2(x)*sin(n*theta) end proc; W := proc (x, theta) options operator, arrow; f3(x)*cos(n*theta) end proc; n := 1; m := 4; len := 1; h := len/m; nn := m+1
 ############################Define some equation

eq1[k_] := -2*f1[k]*(-A11*n^4+A10*n^2+A12*omega^2)*h^4+(A6*(f2[k-1]-f2[k+1])*n^3+A9*(f3[k-1]-f3[k+1])*n^2-A5*(f2[k-1]-f2[k+1])*n-A8*(f3[k-1]-f3[k+1]))*h^3+(4*(f1[k]-(1/2)*f1[k-1]-(1/2)*f1[k+1]))*(A3*n^2-A2)*h^2+(-A4*(f2[k-2]-2*f2[k-1]+2*f2[k+1]-f2[k+2])*n-A7*(f3[k-2]-2*f3[k-1]+2*f3[k+1]-f3[k+2]))*h+12*A1*(f1[k]+(1/6)*f1[k-2]-(2/3)*f1[k-1]-(2/3)*f1[k+1]+(1/6)*f1[k+2]):
  ``

 

 

 

 

                                     ######################################  APPLY BOUNDARY CONDITIONS

f1[nn+1] := f1[m]:
 

for k from 2 to m do eq1[k_]; eq2[k_]; eq3[k_] end do

-(1/64)*f2[4]+(1/128)*f2[3]+(1/64)*(f3[4]-(1/2)*f3[3])*(omega^2-1)-(1/64)*f1[2]+(1/32)*f1[3]+(1/64)*f1[4]-280*f3[4]-120*f3[2]+300*f3[3]+20*f3[7]

(1)

``



Download fdm-maple.mw

 

Hello everybody,

I would like to ask: How many ways to impose the rank deficiency of a matrix J?

1. First is the determinant(J) = 0

2. Multiply with a non-zero vector V: so that we have J*V = 0;

3. ...to be listed......

 

something about the minors of the matrix? 

I hope to have as many methods as possible!

Hi, here is the code I used to try to generate all invertible 4x4 matrices over the finite field F_2 = {0.1}. However, when I look at the elements of GROUP (see below) all the elements are 4x4 matrices with a 2 in each entry. I don't know why this is?

Also, I need help converting all of the invertible 4x4 matrices in the following way: I want the 4x4 matrices to each be written as a string of length 16 with no spaces, commas or brackets. So for example the matrix

a b c d

e f g h

i j k l

m n o p

becomes abcdefghijklmnop

restart:
with(LinearAlgebra):
PRIME := 2;
2

# the group of invertible 4 x 4 matrices over the field F_p

GROUP := []:
M := Matrix([[a,b,c,d],[x,f,g,h],[y,j,k,l],[m,n,o,p]]):
for a from 0 to PRIME-1 do
for b from 0 to PRIME-1 do
for c from 0 to PRIME-1 do
for d from 0 to PRIME-1 do
for x from 0 to PRIME-1 do
for f from 0 to PRIME-1 do
for g from 0 to PRIME-1 do
for h from 0 to PRIME-1 do
for y from 0 to PRIME-1 do
for j from 0 to PRIME-1 do
for k from 0 to PRIME-1 do
for l from 0 to PRIME-1 do
for m from 0 to PRIME-1 do
for n from 0 to PRIME-1 do
for o from 0 to PRIME-1 do
for p from 0 to PRIME-1 do
if Determinant(M) mod PRIME <> 0 then
GROUP := [ op(GROUP), M ]
fi
od od od od od od od od od od od od od od od od:


nops(GROUP);
20160

GROUP;

I want to set the determinant of the coefficient matrix equal to zero and then solving for the roots. But I could not achieve it via Maple. Can you help me please? 

You can reach two examples in the following file.  Yeni_Microsoft_Word_Belgesi_(2).docx

 

Besides. how can i compute the following transcental equations via maple 

 

sinh(beta*L)*sin(beta*L)=0

 

cosh(beta*L)*cos(beta*L)-1=0

 

cosh(beta*L)*cos(beta*L)+1=0

 

regards

mehmet

 

not the same ordering every time of monomials after determinant and map sign positive and op in maple 15

sometimes i need to use Reverse or Rotate List to adjust.

why ordering is different in list of monomials?

is it caused by virus?

 

 from determinant's polynomial?                                                                                                       

I tried to make a procedure that would find the determinant of any 3x3 matrix but I keep getting unterminated procedure what should I change??

Code:
DeterminantMat:=proc(matA::Array)
    local  i::integer,  j::integer,  x::integer,  y::integer,  A::integer,  B::integer,  indice::integer,  S::integer:
      A:=0:  B:=0:  S:=0: i:= 1:  j:=1:  x:=1:  y := 1:  indice:=1:

for x from 1 to 3 do
   indice := 1:  
   for i  from 1 to  3 do  
       if x = i then
           end do:
        else if x <>i then
           for j from 1 to 3 do
                  if y = j then  end do:  
                  else if indice = 1 then  A := matA(i,j):  indice := 2:  
                     else if indice = 2 then  B:=matA(i,j):  indice :=3:    
                       else if indice = 3 then  B :=B * matA(i,j):  indice :=4:    
                         else if indice = 4 then  A := A * matA(i,j):      
                             if x = 2 then  S := S + (-1 * matA(x,y)) * (A-B):
                               else  S := S + matA(x,y) * (A-B):   end if:   end if:
 end do:
 end if:
 end do:
 end do:
 end proc:

hi.after calculate Determinant of matrix  and gain value omega'' ω'' by fsolve rule ,when substuting result (ω) in matrix (q) and calculate Determinant again, this value is not zero!!!! may i use LUDecomposition?determinan.mw

hi...amount of Determinant  is infinity?how i can remove this bad calculation ?

thanks...mode_shape2.mw

I have a multivariate polynomial in x and y. How can I firstly collect the terms with respect to the powers of x and y and then simplifying their coefficients.

restart

with(RealDomain):

with(LinearAlgebra):

A := Matrix(5, 5, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 1, (1, 4) = 1, (1, 5) = 1, (2, 1) = 1, (2, 2) = 0, (2, 3) = c__1, (2, 4) = y, (2, 5) = c__2, (3, 1) = 1, (3, 2) = c__1, (3, 3) = 0, (3, 4) = c__3, (3, 5) = x, (4, 1) = 1, (4, 2) = y, (4, 3) = c__3, (4, 4) = 0, (4, 5) = c__4, (5, 1) = 1, (5, 2) = c__2, (5, 3) = x, (5, 4) = c__4, (5, 5) = 0})

Matrix(%id = 4510803138)

(1)

B := Determinant(A)

-2*c__1^2*c__4+2*c__1*c__2*c__3+2*c__1*c__2*c__4-2*c__1*c__2*x+2*c__1*c__3*c__4-2*c__1*c__3*y-2*c__1*c__4^2+2*c__1*c__4*x+2*c__1*c__4*y+2*c__1*x*y-2*c__2^2*c__3-2*c__2*c__3^2+2*c__2*c__3*c__4+2*c__2*c__3*x+2*c__2*c__3*y-2*c__2*c__4*y+2*c__2*x*y-2*c__3*c__4*x+2*c__3*x*y+2*c__4*x*y-2*x^2*y-2*x*y^2

(2)

``

 

Download A.mw

Hi all,

I need to solve det[M]=0 for omega.

M is:

M := Matrix(8, 8, {(1, 1) = BesselJ(n, tp*a), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = -BesselJ(n, tg*a), (1, 6) = -BesselY(n, tg*a), (1, 7) = 0, (1, 8) = 0, (2, 1) = k*n*BesselJ(n, tp*a)/(tp^2*a), (2, 2) = I*k*n*mu0*omega*(diff(BesselJ(n, tp*a), a))/(tp^2*a), (2, 3) = 0, (2, 4) = 0, (2, 5) = -k*n*BesselJ(n, tg*a)/(tg^2*a), (2, 6) = -k*n*BesselY(n, tg*a)/(tg^2*a), (2, 7) = -I*`&mu;g`*omega*(diff(BesselJ(n, tg*a), a))/tg^2, (2, 8) = -I*`&mu;g`*omega*(diff(BesselY(n, tg*a), a))/tg^2, (3, 1) = 0, (3, 2) = BesselJ(n, tp*a), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = -BesselJ(n, tg*a), (3, 8) = -BesselY(n, tg*a), (4, 1) = -I*omega*`&varepsilon;p`*(diff(BesselJ(n, tp*a), a))/tp^2, (4, 2) = k*n*BesselJ(n, tp*a)/(tp^2*a), (4, 3) = 0, (4, 4) = 0, (4, 5) = I*`&varepsilon;g`*omega*(diff(BesselJ(n, tg*a), a))/tg^2, (4, 6) = I*`&varepsilon;g`*omega*(diff(BesselY(n, tg*a), a))/tg^2, (4, 7) = -k*n*BesselJ(n, tg*a)/(tg^2*a), (4, 8) = -k*n*BesselY(n, tg*a)/(tg^2*a), (5, 1) = 0, (5, 2) = 0, (5, 3) = k*n*BesselY(n, t0*b)/(t0^2*b), (5, 4) = I*mu0*omega*(diff(BesselY(n, t0*b), b))/t0^2, (5, 5) = -k*n*BesselJ(n, tg*b)/(tg^2*b), (5, 6) = -k*n*BesselY(n, tg*b)/(tg^2*b), (5, 7) = -I*`&mu;g`*omega*(diff(BesselJ(n, tg*b), b))/tg^2, (5, 8) = -I*`&mu;g`*omega*(diff(BesselY(n, tg*b), b))/tg^2, (6, 1) = 0, (6, 2) = 0, (6, 3) = BesselY(n, t0*b), (6, 4) = 0, (6, 5) = -BesselJ(n, tg*b), (6, 6) = -BesselY(n, tg*b), (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = BesselY(n, t0*b), (7, 5) = 0, (7, 6) = 0, (7, 7) = -BesselJ(n, tg*b), (7, 8) = -BesselY(n, tg*b), (8, 1) = 0, (8, 2) = 0, (8, 3) = -I*epsilon0*omega*(diff(BesselY(n, t0*b), b))/t0^2, (8, 4) = -k*n*BesselY(n, t0*b)/(t0^2*b), (8, 5) = I*`&varepsilon;g`*omega*(diff(BesselJ(n, tg*b), b))/tg^2, (8, 6) = I*`&varepsilon;g`*omega*(diff(BesselY(n, tg*b), b))/tg^2, (8, 7) = -k*n*BesselJ(n, tg*b)/(tg^2*b), (8, 8) = -k*n*BesselY(n, tg*b)/(tg^2*b)});

and n=0,1,2.

Except of omega and k ,other parameters is canstant.

After using
with(LinearAlgebra):
detM := Determinant(M):

I used solve(detM=0,omega) and fsolve() but it dosnt work. how can i solve it?

Thanks alot.

Hi fellow Maple users,

I'm trying to solve an eigenvalue problem of Ax=wx, where A is a 6 by 6 Hermitian matrix with two parameters x and y. I want to solve it for w and then plot3d it with x and y as unknowns. The way I have been doing is first find the characteristic equation Determinant(A-wI)=0 and then solve it for w, and then plot3d the solutions within a range for x and y. My problem is sometimes solve(Determinant(A-wI)=0,w) would give me the 6 solutions expressed in x and y, but sometimes when the numbers in A are changed it will only give me a Rootof solution with which I cannot plot. I'm wondering if there is a better way to do this. I'm actually not very interested in the symbolic solution of w expressed in x and y, just the plot, so if there is a numerical alternative it's good too.

Thank you in advance!

Hello Everyone

 

I am new to Maple and I have to find the determinant of the following matrix

 

Matrix comprising of Bessel Functions whose determinant is to be calculated

 

https://drive.google.com/file/d/0B_60Jre5scdoSTJ3WUVaMUlidzA/view?usp=sharing

Here k is a constant.

 

Can you please help me with it.

 

Thanks in advance.

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