# Vector Transformation

by nille40
Tags: transformation, vector
 P: 34 Hi! I'm in serious need of some help. I am supposed to show that a transformation $$\mathcal{A} = \mathbb{R}^n \rightarrow \mathbb{R}^m$$ can be separated into $$\mathcal{A} = i \circ \mathcal{B} \circ p$$ where$$p$$ is the projection on the (orthogonal) complement of the kernel of $$\mathcal{A}$$. $$\mathcal{B}$$ is an invertible transformation from the complement to the kernel to the image of $$\mathcal{A}$$. $$i$$ is the inclusion of the image in $$\mathbb{R}^n$$ I hardly know where to start! I would really like some help. I asked this question before, in a different topic, but got a response I didn't understand. I posted a follow-up, but got no response on that. Thanks in advance, Nille