Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Linear Algebra - Linear Transformation

Defn: A function T : V → W is one-to-one (injective) if T(x1)=T(x2)⇒ (x1)=(x2). T is onto (surjective) if T(V)=W.

Thm: If T : V → W is linear transformation, then T is one-to-one iff N(T)={0⃗}.

Let V and W be finite-dimensional vector spaces with dim (W ) = dim (V ) and T : V → W be a linear transformation. Show that T is one-to-one if and only if T is onto.

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