Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + eje}

7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + eje}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

plz

7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + ejef}i<i<i<n U{eie?}i=1...n for symmetric matrices (Hint: This too is in the notes). Explain your answer.
Transcribed Image Text:7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + ejef}i<i<i<n U{eie?}i=1...n for symmetric matrices (Hint: This too is in the notes). Explain your answer.
Th 3.3 i): Let T V W be linear with r = rank (T). Let {w₁,..., w,} be a basis for Rg(T). Let 0; for i = 1,..., r be any choice of elements of V satis- fying T(v₁) = w₁, Vi = 1, ..., r. Let v = nullity (T) and let {₁,..., vy} be a basis for Ker(T). Then {V₁, ..., Ur, U1, ..., U is a basis for V.
Transcribed Image Text:Th 3.3 i): Let T V W be linear with r = rank (T). Let {w₁,..., w,} be a basis for Rg(T). Let 0; for i = 1,..., r be any choice of elements of V satis- fying T(v₁) = w₁, Vi = 1, ..., r. Let v = nullity (T) and let {₁,..., vy} be a basis for Ker(T). Then {V₁, ..., Ur, U1, ..., U is a basis for V.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS