“If the condition number [of a matrix] is not too much larger than one, the matrix is well-conditioned, which means that its inverse can be computed with good accuracy. If the condition number is very large, then the matrix is said to be ill-conditioned. Practically, such a matrix is almost singular*, and the computation of [an ill-conditioned matrix’s] inverse, or solution of a linear system of equations is prone to large numerical errors. A matrix that is not invertible has condition number equal to infinity.” (From “Condition number,” Wikipedia, retrieved 6/3/2020. Emphasis added)
*If a matrix is “almost singular,” then likely that is because it’s determinant is almost zero.
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
