Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
5.1 Pr 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 A = 1 1 2 0 1 Theorem 5.3 Let A be anm x n matrix. Then (a) (aA)+ = a-A*, if a # 0 is a scalar, (b) (A')* = (A+)', (c) (A*)+ = A, (d) A+ = A-1, if A is square and nonsingular, (e) (A'A)+ = A+A+' and (AA')+ = A+'A*, (f) (AA*)+ = AA+ and (A+A)+ = A* A, %3D %3D (h) At = (A'A)-'A' and A+A = In, if rank(A) = n, A 4(AA)-Land A4 (G) A+ = A', if the columns of A are orthogonal, that is, A'A = I,. mif remk(A) = m,

5.1 Pr 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 A = 1 1 2 0 1 Theorem 5.3 Let A be anm x n matrix. Then (a) (aA)+ = a-A*, if a # 0 is a scalar, (b) (A')* = (A+)', (c) (A*)+ = A, (d) A+ = A-1, if A is square and nonsingular, (e) (A'A)+ = A+A+' and (AA')+ = A+'A*, (f) (AA*)+ = AA+ and (A+A)+ = A* A, %3D %3D (h) At = (A'A)-'A' and A+A = In, if rank(A) = n, A 4(AA)-Land A4 (G) A+ = A', if the columns of A are orthogonal, that is, A'A = I,. mif remk(A) = m,

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
5.1 Prove results (a)-(u) 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 The A = 0. 1 1 2 0. 1 Theorem 5.3 Let A be an m x n matrix. Then (a) (aA)+ = a-1A+, if a # 0 is a scalar, (b) (A')* = (A+)', (c) (A*)+ = A, (d) A+ = A-1, if A is square and nonsingular, (e) (A'A)+ = A+A+' and (AA')+ = A+'A*, (f) (AA+)+ = AA+ and (A+ A)+ = A* A, (h) A+ = (A'A)-'A' and At A = In, if rank(A) = n, 44(A4)-Lend A4 (i) A+ = A', if the columns of A are orthogonal, that is, A'A = I. %3D |3D %3D
Transcribed Image Text:5.1 Prove results (a)-(u) 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 The A = 0. 1 1 2 0. 1 Theorem 5.3 Let A be an m x n matrix. Then (a) (aA)+ = a-1A+, if a # 0 is a scalar, (b) (A')* = (A+)', (c) (A*)+ = A, (d) A+ = A-1, if A is square and nonsingular, (e) (A'A)+ = A+A+' and (AA')+ = A+'A*, (f) (AA+)+ = AA+ and (A+ A)+ = A* A, (h) A+ = (A'A)-'A' and At A = In, if rank(A) = n, 44(A4)-Lend A4 (i) A+ = A', if the columns of A are orthogonal, that is, A'A = I. %3D |3D %3D
Expert Solution
steps

Step by step

Solved in 2 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