Linear transformation

Dependencies:

1. Vector Space

Let $U$ and $V$ be vector spaces over field $F$. The function $T: U \mapsto V$ is a linear transformation iff it satisfies both of these conditions:

• $\forall x, y \in U, T(x+y) = T(x) + T(y)$.
• $\forall x \in U, \forall c \in F, T(cx) = cT(x)$.

A linear transformation $T$ is called an isomorphism iff it is bijective. $U$ and $V$ are said to be isomorphic iff an isomorphic linear transformation exists between them.

Dependency for:

1. Kernel of linear transformation is subspace of domain
2. Basis change is an isomorphic linear transformation
3. Vector spaces are isomorphic iff their dimensions are same
4. Matrix of linear transformation
5. Composition of linear transformations
6. Symmetric operator
7. Range of linear transformation is subspace of codomain

Info:

• Depth: 4
• Number of transitive dependencies: 4

Transitive dependencies:

1. Group
2. Ring
3. Field
4. Vector Space