Prove the following statement and illustrate it with examples ofyur own choice.

Question

Prove the following statement and illustrate it with examples ofyur own choice. Her 1,.....,n are the (not necessarilydistinct) eigenvalues of a given n*n matrix A=[ajk]

The "polynomial matrix"
p(A) =kmAm+km-1Am-1+....+k1A+ko

has the eigenvalues

p(1) = kmjm+km-1im-1+.....+k1j+k0


where j = 1,2,....,n and the same eigenvestors as A

Explanation / Answer

x.P5style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; list-style-type: none; list-style-position: initial; list-style-image: initial; ">Question Details: Prove the following statement and illustrate it with examples of yur own choice. Her 1,.....,n are the (not necessarily distinct) eigenvalues of a given n*n matrix A=[ajk] The "polynomial matrix" p(A) = kmAm+km-1Am-1+....+k1A+ko has the eigenvalues p(1) = km&

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.