Conclude that there is a vital assumption when using rank nullity, often overlooked. What isit?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?

According to Rank-nullity theorem, if V and W are vector spaces and T is a linear operator from V…

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?

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?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter5: Graphs And The Derivative

Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test

Problem 87E

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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?

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