Composition of Linear Maps — Topic Summaries
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Linear Algebra 19 | Matrices induce linear maps
A matrix isn’t just a table of numbers: it automatically defines a linear map between vector spaces, and the usual matrix-vector multiplication is...
Linear Algebra 31 | Inverses of Linear Maps are Linear
An invertible linear map has an inverse that is automatically linear—a fact that removes a whole class of checks when working with linear...
Abstract Linear Algebra 23 | Combinations of Linear Maps
Linear maps aren’t just single functions between vector spaces—they form their own vector space under addition and scalar multiplication. Given two...
Linear Algebra 31 | Inverses of Linear Maps are Linear [dark version]
Inverses of bijective linear maps are themselves linear—so once a linear map is invertible, there’s no need to re-check linearity for its inverse....