Conclude that there is a vital assumption when using rank nullity, often overlooked. What is it? Let B = {b} form a basis for V, and T:V → V is linear "operator". Suppose EB,T(b;) is defined. Is T a well defined function? Can you relate this concept to diagonalizability?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
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Conclude that there is a vital assumption when using rank nullity, often overlooked. What is
it?
Let B = {b}=₁ form a basis for V, and T:V → V is linear "operator".
Suppose EB, T(b) is defined. Is T a well defined function?
Can you relate this concept to diagonalizability?
Transcribed Image Text:Conclude that there is a vital assumption when using rank nullity, often overlooked. What is it? Let B = {b}=₁ form a basis for V, and T:V → V is linear "operator". Suppose EB, T(b) is defined. Is T a well defined function? Can you relate this concept to diagonalizability?
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