Function to find if B is an echelon or row equivalent of A

Hello, Im new to MATLAB and would like to know which function should I use if matrix B is row-equivalent of matrix A, and the function that calculates if matrix B is one of the valid echelon forms of matrix A

Thanks

Answer 1

[Aurelien Queffurust]

Let's say B has the same second row of A :

   >>A = [1 2 3; 4 5 6; 7 8 9];
   >>B = [ 4 5 6;10 11 12];

You could use ismember to have this equivalent :

    >> ismember(A,B)

ans =

       0     0     0
       1     1     1
       0     0     0

Answer 2

[Andrei Bobrov]

tstg - function of test of gaussian elimination products

tstg = @(A,B)abs(mod(det([A(1:end-1,:);B]),det(A))) < 1e6*eps;

eg:

>> A= randi(78,3)
A =
    70    11    66
    75    12    20
    43    21    64
>> B = randi(78,1,3)
B =
    19    73    28
>> tstg(A,B)
ans =
     0

>> B = A(1,:)*2 + A(3,:)
B =
   183    43   196
>> tstg(A,B)
ans =
     1

ADD [09:23(UTC+4) 30.12.2011]

e.g.

A = randi(8,9,5);
B = A(1,:)*.4+A(end,:)*8;

K = nchoosek(1:size(A,1),size(A,2)-1);
out = [];
flag = false;
for i1 = 1:size(B,1)
    b = B(i1,:);
    for j1 = 1:size(K,1)
        if abs(det([A(K(j1,:),:);b])) < 1e3*eps
            flag = true;
            out = [out; j1 i1];
        end
    end
end

[Husy]

Andrei, Thanks for the response. I get the following error

>> tstg(A,B)

??? Error using ==> det

Matrix must be square.

Error in ==> @(A,B)abs(mod(det([A(1:end-1,:);B]),det(A)))<1e6*eps

Answer 3

[Husy]

Aurelien, Thanks for response. Your answer is for the question "Does B contain a row that is equal to a row of A". My question is row equivalance, not equal. By row equivalance, I mean that the row in B, is a product of gaussian elimination done on corresponding row in matrix A. For example

          >>A = [1 2 3; 4 5 6; 7 8 9];
          >>B = [1 2 3;1 -1 -3;7 8 9];

In this example BRow2=ARow2 - 3 *ARow1 So Matrix A and B are row equivalant, since B is a product of gaussian elimintaion done on matrix A

Answer 4

[Andrew Newell]

function TF = areRowEquivalent(A,B,tol)
TF = norm(rref(A)-rref(B)) < tol;

EDIT: Take the two lines and save them in a file called areRowEquivalent.m. Here is an example of its use. The function returns a logical value (true/false), and I have added some code to interpret it in words.

A = [1 2 3; 4 5 6; 7 8 9];
B = [1 2 3;1 -1 -3;7 8 9];
tol = 1e-6;

TF = areRowEquivalent(A,B,tol);
if TF
  disp(['Row equivalent to a tolerance of ',num2str(tol),'.'])
else
  disp(['Not row equivalent to a tolerance of ',num2str(tol),'.'])
end

[Husy]

Andrew,

I believe this is the answer I need, but since I am new to MATLAB (But I know algorithms), I am not able to make this work.

I pasted this code exactly then got an error.

Then I googled and found smthng, I saved this as areRowEquivalent.m file in my work path.

But now how should I use this function?

I tried some workarounds but got error about tol, what is tol used for here?

Thanks

[Andrew Newell]

Husy, I have edited my response to provide more information.