A proxy for this value, called its “stable” variant, equals the square of the Frobenius norm divided by the square of the spectral norm. The reduction of this quantity is most efficiently performed by truncating a singular value decomposition according to the Eckart-Young theorem. If an object has a value of k for this quantity, then its minimal polynomial may have degree up to k plus 1. The (*) outer product of two nonzero vectors u and v always has a value of 1 for this quantity. This quantity and the nullity sum to the number of columns in a matrix. An n-by-n matrix has a value of n for this quantity if and only if it is invertible. The “row” and “column” varieties of this quantity are equal for any matrix. For 10 points, name this quantity which is the dimension of a matrix’s column or row space. ■END■
ANSWER: rank [accept row rank or column rank; accept rank-nullity theorem; accept low-rank approximation; accept stable rank; accept any description of the dimension of a vector space spanned by its columns before “dimension”; prompt on dimensions]
<Alex Li, Other Science>
= Average correct buzz position