Further, all the maximal algebraically independent subsets have the same cardinality, known as the transcendence degree of the extension.

Thus, a set of linearly dependent vectors is redundant in the sense that a linearly independent subset will span the same subspace.

Try seeing what happens if you use independent subsets of your data for estimation and apply those estimates to the whole data set.

There are several ways to choose a maximal independent subset consisting of equations.

The set of all linearly independent subsets of a vector space V, ordered by inclusion.

The column matroid of this matrix has as its independent sets the linearly independent subsets of columns.

Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K.

Such independent subsets are called partite sets, or simply parts.

Then is a linearly independent subset of V.

A basis B of a vector space V over a field F is a linearly independent subset of V that spans V.