How to get a constant multiplier of any matrix using same matrix ???

Let A be the m x n matrix.

I need a matrix such that B = k.A or det(B) = k.det(A)

where k is defined as 1 < k < infinite . It can be both integer and non-integer.

[Walter Roberson]

Does k have a definite value at each point, or do you need it as an indefinite variable to be reasoned about?

If you need it as an indefinite value to be reasoned about then you will need to use the symbolic toolbox.

[David Goodmanson]

Hi Manoj,

Depending on how 'or' is interpreted, B = k*A and det(A) = k*det(B) could be in conflict, since B = k*A implies det(B) = k^n*det(A). And of course for any dets, n=m.

[Manoj Kumar]

Actually we decide the value of k or its value should controllable by us.

[Manoj Kumar]

David u are right. It says the marix properties.

[Walter Roberson]

K.*A

and

K*A

would both multiply A by k

[Manoj Kumar]

it is not just constant is multiply to matrix A.

A => mxn diamension

Actually I want to make a matrix such that

B = function(A), having same diamension mxn, but the resultant matrix B is given by B = k.A.

Here we have to do matrix manipulation to achieve constant parameter k.

The choice of k (constant) will be decided by us preferably.

[Walter Roberson]

B = @(A) k.*A;

[Manoj Kumar]

Actually I'm searching a function in matlab which can give the required result. B is a matrix purely formed by matrix A, either by multiplication, inverse , transpose or conmbination of any three.

The resultant form of B will be constant.A.

e.g A = [1 2 3; 4 5 6; 7 8 9]

then B = 8*[1 2 3; 4 5 6; 7 8 9]

Here 8 is not multiplied to A, but obtained by Playing with matrix A using multiplication, inverse or/and transpose operation.

[Walter Roberson]

So the input is just A? How should it decide on k? Could give an example of the case where B is formed by inversion of A but is still constant times A?

[Walter Roberson]

What does the "." operator mean in B = k.A ?

I think we need to see at least two examples worked through.

[Manoj Kumar]

1) I am thinking about this case only. How I'll get, I don't know.

2) Here dot(.) means simple multiplication in math.

e.g A = [1 2 3; 1 2 1; 2 1 3]

then B = 8*[1 2 3; 1 2 1; 2 1 3] = [8 16 24: 8 16 8; 16 8 24 ]

Do you think any such matrix can be make ?

[Jan]

@Manoj Kumar: I still do not understand, what you are asking for. All I understand is that you want to multiply the matrix A by a constant k. Then B = k*A is the trivial solution. But what is the problem then?

Please explain it again: What are the given inputs? Matrix A and what? B or k? What is the wanted output?

[Steven Lord]

Manoj Kumar, please fill in the blanks in this statement, be very clear and explicit when you fill them in, and add additional blanks in the middle if necessary.

The only operations I am allowed to use in this assignment are __________________, ___________________, and _________________________.

Alternately, since this sounds like a problem a professor might assign as homework, if it is copy the text of the assignment verbatim into a comment to help us understand the constraints your professor has placed on you.

[Manoj Kumar]

S. Lord,

I'm truely saying it's not any assignment work given by anybody.

It is my thinking, requirement , when I ploting a matlab code.

I also need such a problem solution. Why I'm asking? Because I thinking anyone who has well understanding of matlab can suggest its solution.

If we able to design such a function using single matrix, in the same time we able to control the response by allowing all matrix properties.

[David Goodmanson]

per Walter's query, some matrices that are proportional to their inverse.

a) all 2x2 traceless matrices with nonzero determinant

b) rotation matrices by 180 degrees about an arbitrary axis

c) in the following example, to avoid numerical innacuracy (which turned out to be very small anyway) in taking the inverse,

% M*M = k*I  --> M = k*inv(M)  (assuming inverse exists)

M =  [263   106    54  -196  -106
      368   -87    12  -132  -112
      286   -86     5  -254    86
      274   118   -30  -267  -118
      286   -86   204  -254  -113]

M*M

ans =  39601           0           0           0           0
           0       39601           0           0           0
           0           0       39601           0           0
           0           0           0       39601           0
           0           0           0           0       39601 

.

Answer 1

[Walter Roberson]

function B = generate_B(A)
   maxval = realmax ./ max(abs(A(:)));
   while true
       k = typecast(randi([0 255], 1, 8, 'uint8'), 'double');
       if isfinite(k) && abs(k) <= maxval; break; end
   end
   B = k * A;
end