inv (J
Well, it has a column of zeros
And while I do believe he was exaggerating, it did make me curious about just how many reasons (the determinant's being zero A commonly used trick is to add a very small constant (e
I just want to add some comments on Matrix Condition Number, which we can use to check the numerical stability issues
We say that a matrix is singular if it’s not invertible; it doesn’t have an inverse
As it has been clarified in the comments and answers above, seeking the inverse of a nearly singular matrix is meaningless
What this means is that its inverse does not exist
Solve that
I have a problem of making a slight change on a singular matrix to make that matrix become full rank
For example, if you want your resulting matrix to be close to the original in the $2$-norm sense, you can find the singular value decomposition of the matrix first, then remove singular vectors corresponding to zero singular values
This mean that the matrix I − A I − A is invertible (non-singular) and it's inverse is I + A I + A
A common way to do that is using the method of least squares
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A singular matrix is one that is not invertible
To add two matrices: add the numbers in the matching positions: These are the calculations: 3+4=7
e
What are singular matrices and what does a singular matrix mean are a few of the questions explored in this video
Viewed this way, idempotent matrices are idempotent elements of matrix rings