Linear Transformation

up:: Vector Space

Let be vector spaces over the same Field . A transformation is said to be a linear transformation if

Thus, it preserves the vector space operations from to .

Properties

• If , we say that is an Endomorphism.
• A linear transformation is injective iff its kernel is trivial
• A linear transformation’s image of a basis spans its image
• A linear transformation is injective iff it preserves linear independence
• A linear transformation between spaces of equal dimension is injective iff it’s surjective iff it’s an isomorphism

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References

• Notas sobre Álgebra Linear