← MATH 01210 · Linear Algebra
MATH 01210 · Linear maps & eigenstuff
Matrix of a linear transformation
Definition
A linear map T:Rⁿ→Rᵐ satisfies T(u+v)=T(u)+T(v) and T(cu)=cT(u). Relative to standard bases, T(x)=Ax for A whose columns are T(eⱼ).
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Composition of maps ↔ matrix multiplication.
Change of basis: A = P B P⁻¹ style relationships for similar matrices.
Kernel and image of T match null and column spaces of A.
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1.Find matrix of T(x,y)=(x+y, 2x) on R².