linear vocab

span

the ___ of vectors v1…vn is the set of all possible linear combinations of v1…vn

linearly independent

a set of vectors v1…vn is ___ if the system x1v1+…+x vn has only the trivial solution x1=x2=…=xn=0

linear transformation

a ___ T is a transformation that maps from R^n to R^m, satisfying T(au+bv) = aT(u) + bT(v), where a and b are scalars in R, and u and v are vectors in R^n

one to one

a function f: X → Y is ___ if when x ≠ y, then f(x) ≠ f(y) for any x, y in X

Onto

a function f: X → Y is ___ if for every y in Y, there exists an x in X such that f(x) = y

invertable

a square matrix A (nxn) is ___ if there exists an nxn matrix B such that AB=BA=I_n