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> - A basis set of column vectors Let's leave the word 'basis' out, since the column vectors may well be linearly dependent.
by JadeNB 7y ago
> - A basis set of column vectors
Let's leave the word 'basis' out, since the column vectors may well be linearly dependent.
- FabHK 7y agoOr not span the space, for that matter.
- JadeNB 7y agoWell, it depends on what "the space" is. Every set of vectors (in a common ambient space) spans some space—often called the column space of a matrix, if they are the column vectors of the matrix.
- FabHK 7y agoSure, every set of vectors will span the space they span. But the requirement that a basis span the space refers to the space it’s in, not the space it spans (otherwise every linearly independent set of vectors were a basis, spanning the space it spans.) I could go on :-)