Learning starts with a question
First time here? Checkout the FAQs!
x

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO


MathsGee Android Q&A

0 like 0 dislike
230 views
An \(n \times n\) matrix is called nilpotent if \(A^{k}\) equals the zero matrix for some positive integer \(k\). (For instance, \(\left(\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right)\) is nilpotent.)
a) If \(\lambda\) is an eigenvalue of a nilpotent matrix \(A\), show that \(\lambda=0\). (Hint: start with the equation \(A \vec{x}=\lambda \vec{x}\).)
b) Show that if \(A\) is both nilpotent and diagonalizable, then \(A\) is the zero matrix. [Hint: use Part a).]
c) Let \(A\) be the matrix that represents \(T: \mathcal{P}_{5} \rightarrow \mathcal{P}_{5}\) (polynomials of degree at most 5) given by differentiation: \(T p=d p / d x\). Without doing any computations, explain why \(A\) must be nilpotent.
in Mathematics by Platinum (147,718 points) | 230 views

Related questions

0 like 0 dislike
0 answers
1 like 0 dislike
1 answer
0 like 0 dislike
1 answer
asked Jul 24, 2021 in Mathematics by MathsGee Platinum (147,718 points) | 160 views

Join MathsGee, where you get quality STEM education support from our community of verified experts fast.


On the MathsGee, you can:


1. Ask questions


2. Get expert answers


3. Vote on questions and answers


4. Tip your favorite community members


5. Join expert live video sessions (Paid/Free)


6. Earn points by participating



Posting on MathsGee


1. Remember the human


2. Act like you would in real life


3. Find original source of content


4. Check for duplicates before publishing


5. Read the community guidelines




MathsGee Rules


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.




MathsGee Android Q&A

MathsGee Android Q&A