Dear all
To best of my knowledge, if columns of a matrix are highly-correlated, then this matrix will have a large condition number. I'll really appreciate if you provide me with other underlying causes of condition number increasing.
I think that next link is a good introduction:
https://en.wikipedia.org/wiki/Condition_number
As for matrices, if a column (or row) is close to be a linear combination of other(s) column(s) (or row(s)) then condition number tends to infinity.
I think that next link is a good introduction:
https://en.wikipedia.org/wiki/Condition_number
As for matrices, if a column (or row) is close to be a linear combination of other(s) column(s) (or row(s)) then condition number tends to infinity.
any matrix A, can be decomposed into a sum of rank one matrices with weightage factor for each component matrix is the singular value associated with that pair of 1 dimensional subspaces (the 1 dim. subspace of row space and the 1 dim subspace of the column space that are interlinked by ATRANSPOSE*A and A*ATRANSPOSE Matrices. Near singular component matrices relate to those subspace pairs whose weightage, i.e the associated singular value is non zero, but extremely small, it is these near singular components in the Singular value decomposition of the matrix A that result in ill conditioning of the matrix A.
A matrix has very high condition number means that the matrix is nearly singular. This, in turn, implies that one or more columns are close to linear combinations of the rest of the columns.
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