Linear algebra - Memorising proper definitions of homomorphism types I am reading a book about linear algebra. On the basis of this book, I worked out the terminology below. Problem: To me, it looks like Wikipedia defines homomorphism differently. Apart from that: Do you agree with the following definitions of the homomorphism subtypes?
If so, is there a trick to memorise them?

Let $V_1, V_2$ be vector spaces over a common field.
We consider a function
$f : V_1 \rightarrow V_2$.
Now, $f$ is a homomorphism iff $f$ is linear (linear-algebra-linear, not calculus-linear).
epimorphism =
homomorphism +
surjective
monomorphism =
homomorphism +
injective
isomorphism =
epimorphism +
monomorphism
endomorphism =
homomorphism +
(domain = codomain)
automorphism =
endomorphism +
isomorphism

The article Algebra homomorphism enumerates (in its first sentence) homogeneity and additivity but also a third property. The third property seems to be missing in my definition (definition based on the book).
By the way, should I use the term map instead of function?
 A: As for "how do you remember them?":
Every single one of those words is self-explanatory if you have a basic knowledge of Greek and Latin roots in English. This site is pretty handy, as would any dictionary.* (These might all be Greek: I didn't check.) 


*

*"homo-" meaning "same"  (think about what homogenization means)

*"epi" meaning "upon"     ("epidemic"/"epicenter")

*"mono" meaning "one"     ("monologue")

*"iso" meaning "identical/equal" ("isobar")

*"endo" meaning "inside/inner" ("endoskeleton"))

*"auto" meaning "self"     ("automobile")


and finally "morphism" meaning "form/shape".
Every category of objects has its own special version of these things. The one thing that changes in between categories is what the morphism preserves. 
A morphism is only good for that algebraic category if it preserves the basic features of the objects. So for example in the category of groups, a homomorphism only has to preserve the product. For rings, it has to preserve both operations. For algebras, it has to preserve both operations and it has to be linear with respect to the field. For vector spaces it has to preserve addition and scaling. 
$^\ast$ Actually, I took a college course on Greek and Latin roots in English, and I would recommend it to any student: it's really useful.

Addendum: As for "function" versus "map": they are usually interchangeable. Some specific books or disciplines might find different uses for them, but in most contexts they mean the same thing.
A: You found a different definition of homomorphism because you were looking at the wiki page on Algebras.  If you want an explicit definition of "homomorphisms between vector spaces", you should be looking at the definition of module homorphisms.  
The main difference between modules and algebras is that in algebras (unlike in modules, and in particular, vector spaces) you are able to multiply two elements.  Notice, however, that if we take the definition of homomorphisms and disregard the multiplication of two elements (since you can't multiply vectors), then this just gives you linearity.
The definitions you have written are certainly correct in the context of linear algebra.  However, all of these terms have slightly more general definitions that used in algebraic topics such as category theory.
