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Codomain
A set containing all possible outputs for a function. (Note that this contains the range, which is equal to the set of possible outputs for a function.)
Domain
The set of possible inputs for a function
Image
The output of a function from a particular input
Linear transformation
A function T : Rm → Rn is a linear transformation if for all vectors u and v in Rm and all scalars r we have;
T(u + v) = T(u) + T(v)
T(ru) = rT(u)
Matrix dimensions
The number of rows and columns for a matrix. Generally displayed as n × m, where n is the number of rows and m the number of columns
One-to-one
A linear transformation T : Rm → Rn is one-to-one if for every vector w in Rn there exists at most one vector u in Rm such that T(u) = w. Alternate definition: A linear transformation T is one-to-one if T(u) = T(v) implies that u = v.
Onto
A linear transformation T : Rm → Rn is onto if for every vector w in Rn there exists at least one vector u in Rm such that T(u) = w
Range
The set of outputs for a function
Square matrix
matrix with the same number of rows and columns