I just learnt about vector space in linear algebra, and I think i misunderstood the meaning of vector in linear algebra. Can you help me please?
A vector in linear algebra is generally just a list of components. In two dimensions these would represent the x and y components if you think of them graphically. However, in general, there could be n terms, where n is much greater than 2, so these would be difficult to visualise! The components are usually listed within brackets. When these are aligned in a row you have a row vector; when they are aligned vertically, you have a column vector. There are specific rules for adding, multiplying etc.
Is this what you are looking for, or is there a specific feature you encountered that puzzled you?
Oneof the things that puzzled me is that the lecturer said a vector can be expressed by a function, or that a function can be represented by a vector, or that functions and vectors are the same. Im not quite sure tho.
You could certainly have functions of vectors. You could have functions that generate the components of vectors. Without knowing exactly what your lecturer meant by "expressed by" though, I'm not going to be a great help!