The ratio of max svd to min svd is not a clear criterion to figure out how many columns are linearly-dependent on other columns. The best criteria is to sort svd values ascending and start from the beginning of the array, check the ratio of each pair of neighbor svd values.... An easy exclusion criterion is a matrix that is not nxn. Only a square matrices are invertible (have an inverse). For the matrix to be invertible, the vectors (as columns) must be linearly independent.
If the matrix is invertible, the pseudoinverse will be the inverse. However, if you are seeing non-invertible matrixes, chances are that your distance from the cluster will be meaningless if the vector is outside of the hyperplane the cluster repesents, because you do not know the variance in the orthogonal space (you can think of this variance as 0!)... Because det(AB)=det(A)det(B), the determinant of the inverse is the reciprocal of the original determinant. Therefore if the inverse and original both have whole number entries, then det(A) must be a whole number whose reciprocal is a whole number.
What to do when sample covariance matrix is not invertible?
To calculate inverse matrix you need to do the following steps. Set the matrix (must be square) and append the identity matrix of the same dimension to it. Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one).
5/10/2016 · Note that for a matrix to have an inverse, there must exist both a left inverse and a right inverse. Otherwise, the matrix is said to be noninvertible, or singular. Theorem I.
First, make sure that your matrix is "square". That means, it must be 2x2 or 3x3 or 4x4.... Then, press the Math Templates button (to the right of the number 9, and to the left of the "book") and access the correct shape of the matrix you wish to enter.