Let T be a linear operator on a finite-dimensional vector space V for which the distinct eigenvalues 11, 12,..., 4 occur with multiplicities m1, m2,.., m, respectively. If B is a basis for V such that [T], is a triangular matrix, prove that the diagonal entries of [T], are A1, 12, occurs m, times (j= 1,2,..., k). d and that cach 2, ....
Let T be a linear operator on a finite-dimensional vector space V for which the distinct eigenvalues 11, 12,..., 4 occur with multiplicities m1, m2,.., m, respectively. If B is a basis for V such that [T], is a triangular matrix, prove that the diagonal entries of [T], are A1, 12, occurs m, times (j= 1,2,..., k). d and that cach 2, ....
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let T be a linear operator on a finite-dimensional vector space V for which
the distinct eigenvalues 11, 12,..., 4 occur with multiplicities m1, m2,..,
m, respectively. If B is a basis for V such that [T], is a triangular matrix,
prove that the diagonal entries of [T], are A1, 12,
occurs m, times (j= 1,2,..., k).
d and that cach 2,
....](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5944101-e157-4f88-8773-ec8eac72015c%2F3df7e7f0-13e4-4191-99ea-037294753e23%2Fsiyiedjr.jpeg&w=3840&q=75)
Transcribed Image Text:Let T be a linear operator on a finite-dimensional vector space V for which
the distinct eigenvalues 11, 12,..., 4 occur with multiplicities m1, m2,..,
m, respectively. If B is a basis for V such that [T], is a triangular matrix,
prove that the diagonal entries of [T], are A1, 12,
occurs m, times (j= 1,2,..., k).
d and that cach 2,
....
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