# I How this defines a linear transformation

Tags:
1. Apr 25, 2016

### Granger

Admit that $$V$$ is a linear space about $$\mathbb{R}$$ and that U and W are subspaces of V. Suppose that $$S: U \rightarrow Y$$ and $$T: W \rightarrow Y$$ are two linear transformations that satisfy the property:

$$(\forall x \in U \cap W) S(x)=T(x)$$

Define a linear transformation $$F: U+W \rightarrow Y$$ that matches with S for values in U and matches with T with values in W.

My thought is to choose the linear transformation $$F=S+T$$ because it will be the union of both transformation, right? But we have the problem that when our objects are in the intersection of both space we will get to F = 2S instead of S

Last edited: Apr 25, 2016
2. Apr 25, 2016

### Stephen Tashi

On this forum the tags using backslash and "tex" don't work for LaTex. Use a forward slash.

Are you asking whether it is possible to define such a linear transformaton ?

3. Apr 25, 2016

### Granger

Hello Stephen!

Thanks, I edited my question.

No, I know it's possible to define the linear transformation I'm asking what should be the linear transformation and how can I get there :)

4. Apr 25, 2016

### jbunniii

Do you know about direct sums, and complements of subspaces?