Linear Transformation

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date: 2025-01-10

Theorem

a. Vector space form Let are finite dimensional spaces and . There are bases of and respectively such that the matrix of looks like ,

Let is a basis for kerT we can extend this to a basis let is a basis for extend this to a basis of say

Theorem

. Matrix form: if matrix then invertable and Such that is of the form

is a sequence of column operations and a sequence of row operations

Remark

^e78495 and ^71b964 are equivalent.

^e78495 ^71b964 If holds Let be a matrix over ^71b964^e78495 If holds Let A be the matrix associated with with basis and we get let and