# Linear algebra identity evaluation

I really couldn't find anything related to this simple identity I came up with so:

$$\vec{r}=(r_x,r_y)=(r_x, \angle0)+(r_y,\angle\frac{\pi}{2})$$

My thinking process was that $$r_y$$ is practically the modulus of a vector in the Y axis (or with $$\theta=90°=\frac{\pi}{2}$$) and $$r_x$$ is the modulus of a vector in the X axis (or with $$\theta=0°=0$$).

Is this true? I'm sorry if this is obvious or this question is repeated or easy to look up; I'm new to linear algebra and I don't know what to expect or how to search for stuff.

The statement $$\vec{r}=(r_x,r_y)=(r_x, \angle0)+(r_y,\angle\frac{\pi}{2})$$ Is equivalent to the statement that $$\mathbf{r}=\begin{bmatrix}r_1 \\ r_2 \end{bmatrix}= r_1\begin{bmatrix}1 \\ 0 \end{bmatrix} + r_2\begin{bmatrix}0 \\ 1 \end{bmatrix} = r_1 \mathbf{\hat i} + r_2\mathbf{\hat j}$$ where $$\mathbf{\hat i}$$ and $$\mathbf{\hat j}$$ are the standard basis of $$\mathbb R^2$$. You will note that any $$n$$-dimensional vector can be expressed as a linear combtination of some $$n$$ independent basis vectors. In fact, each component $$v_i$$ of a vector can be conceptulized as the factor by which the $$i$$th basis vector of a vector space must be scaled when producing the vector.
This property is true for greater dimensions that $$2$$, and can be extended to vector spaces besides $$\mathbb R^n$$. This concept is fundamental to understanding linear algebra. Matrices, for instance, can be understood as linear transformations of space, where the $$i$$th column of the matrix describes where the $$i$$th basis vector "lands" after moving through the transformation.