What is the term for 2 vectors at 45 degree angle to each other When two vectors in a 2 dimensional space are collinear, they are linearly dependent. When they are perpendicular ,they are linearly independent because you cannot get one from the other by a linear transformation.
If these 2 vectors are at a 45 degree angle between them ,are they considered semi independent? What is the math term for this?
 A: Linearly independent does not mean that one is not the image of the other under a linear transformation. For any two vectors we can always find a linear transformation that takes one to the other. (Maybe you meant scalar multiplication. "Linear transformation" is a much broader term).
A set of vectors is linearly independent when none of the vectors can be expressed as a linear combination of the others. That is, it is never the case that $$\vec{v}_i = \sum\limits_{j \ne i} a_j\vec v_j$$
for any scalars $a_i$. This usually is expressed more simply by saying that the vectors $\vec v_i$ are linearly independent if and only if whenever
$$0 = \sum_i a_i\vec v_i$$
it must be the case that $a_i = 0$ for all $i$.
In two dimensions, any set of 3 or more vectors is linearly dependent (that is why it is 2 dimensions). For two vectors to be linearly dependent, we have to have
$$0 = a\vec v_1 + b\vec v_2$$
with either $a$ or $b$ not zero. If $a$ is not zero, then you can rewrite this as $\vec v_1 = \frac{-b}a\vec v_2$, and similarly when $b$ is not zero. In other words, the only for two vectors to be linearly dependent is for one to be a multiple of the other.
Two vectors that are multiples of each other point in the same direction or the opposite direction. Thus two vectors are linearly dependent only if the angle between them is either $0^\circ$ or $180^\circ$. All other angles, including $45^\circ$, yield independent vectors.
