MATLAB: Replace A single element of matrix

MATLABmatrix manipulation

Hi, what I want to do is replace a single value in the 201X201 identity matrix to form a transformation matrix. I know how to form the identity matrix, but im having trouble figuring out how to replace a value. I want to replace the zero in the 201st row and 1st column with a 240. I know this probably has a an easy solution, but any help is appreciated, thanks!

Best Answer

x(201,1)=240;

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MATLAB: Problem in calculating a determinant for a matrix

Nobody bothered to answer this homework question yet? Return to linear algebra 101.

1. If the determinant of the nxn matrix A is D, then the determinant of the matrix k*A is k^n*D.

2. DON'T USE THE DETERMINANT!!!!!!!!!!!!!! EVER!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Because of 1, it is trivial to create a matrix that will result in any garbage answer that you desire, at least in terms of floating point arithmetic. This is exactly what you have discovered, i.e., a matrix that should be singular, yet returns numerical trash from the determinant.

3. The determinant of a matrix can be written as the product of the eigenvalues. (See 1!) It also can be computed as the product of the diagonals of the U factor from an LU factorization. This is what det does.

Look at the diagonals from the LU factor of the matrix that you have created.

[L,U] = lu(A);
diag(U)
ans =
        100
       -100
       -200
       -300
       -300
       -500
       -600
       -700
       -700
        100
        100
       -200
       -300
        100
       -400
 1.4211e-14
prod(diag(U))
ans =
  -9.0245e+21

See that the matrix is clearly singular. Yet, the one tiny diagonal element, which is numerically zero compared to the rest in terms, is overwhelmed when you form the product.

det(A/100)
ans =
   7.0504e-11

Is the matrix singular? OF COURSE IT IS!

rank(A)
ans =
    15

4. Use rank to determine the rank of a matrix. If you know a little more about linear algebra, then you can use other tools like cond or svd.

cond(A)
ans =
   6.0814e+17

In the end, unless you thoroughly understand det, and know why and when not to use it, you should never use det. And IF you do understand all of this about det, then you should also know why you almost never need to use det!

MATLAB: How to map the lowest 15 grayscale levels to 15 and highest 15 grayscale values to 240 in a 256*256 image

Try this:

grayImage(grayImage < 15) = 15; % Everything 14 and less becomes 15.
grayImage(grayImage > 240) = 240; % Everything 241 and higher becomes 240.

Best Answer

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MATLAB: Problem in calculating a determinant for a matrix

MATLAB: How to map the lowest 15 grayscale levels to 15 and highest 15 grayscale values to 240 in a 256*256 image

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