range & kernel


Summary

Rank and injectivity/surjectivity

Equivalent statements of invertibility

Concept

Range

set of vectors that gets mapped to

Rank

Kernel

set of vectors that map to 0

Nullity

1-1 (injective)

if multiple vectors map to 0, then it cannot be 1-1

onto (surjective)

every is mapped to by at least one

Bijectivity and invertibility

Application