Linear algebra MOC

Linear isomorphism

A 𝕂-linear isomorphism 𝜑 :𝑉 →𝑊 is an isomorphism in 𝖵𝖾𝖼𝗍𝕂, #m/def/linalg i.e. a linear map with a (necessarily unique) two-sided inverse 𝜑−1 :𝑊 →𝑉 such that 𝜑−1𝜑 =1𝑉 and 𝜑𝜑−1 =1𝑊.

Properties

• A linear map 𝜑 ∈𝖵𝖾𝖼𝗍𝕂(𝑉,𝑊) is an isomorphism iff it is a linear monomorphism and split linear epimorphism.
• See Corollaries.

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