Another criteria for injectivity and surjectivity

[Alvant]

Linear map f: X -> Y (dim X = n, dim Y = m), its matrix (in some bases of the spaces) is A.

• f injective <-> Ker f = 0 <-> dim Im f = dim X <-> Rg A = n
• f surjective <-> dim Im f = dim Y <-> Rg A = m
• f bijective <-> Rg A = n = m

Related: #56.

[Alvant]

Maybe someday I'll add it to the seminar notes. Or maybe not. Most likely not. Whatever. You will remain unfinished. So be it. Adiós.

[Alvant]

You know what? To hell with these new criteria! I think you are quite finished as it is.