Finding Least Square Solutions for Singular Matrices

  • Thread starter Thread starter Punkyc7
  • Start date Start date
  • Tags Tags
    Square
Click For Summary

Homework Help Overview

The discussion revolves around finding least square solutions for a system involving a singular matrix. The original poster presents a matrix equation and expresses confusion regarding the solution provided in their textbook.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of plugging values into a formula and the implications of the singularity of the matrix A^tA. Questions arise about the origin of the solution presented in the textbook.

Discussion Status

The conversation includes attempts to clarify the method used and the nature of the solutions due to the singular matrix. Some participants note the existence of an infinite number of solutions, indicating a productive exploration of the topic.

Contextual Notes

There is an emphasis on the singularity of the matrix A^tA, which affects the ability to find a unique solution. The original poster's confusion about the textbook's solution suggests a need for further clarification on the problem setup.

Punkyc7
Messages
415
Reaction score
0
Find the least square solutions x* of the system Ax=bA=[1 3
2 6]

b=[5
0]A^tAx=A^tbSo I get down to
[5 15 [x1 [5
15 45] x2] = 15]

so i get [1
0]

The book says the solution is
[1-3s
s]

not sure were that came from
 
Last edited:
Physics news on Phys.org
can you explain your method?
 
Just plug into the formula the only problem is that the matrix I get by multiplying A transpose A cannot not be inverted
 
Punkyc7 said:
Just plug into the formula the only problem is that the matrix I get by multiplying A transpose A cannot not be inverted

That's because ATA is singular, which in this case means an infinite number of solutions. If you multiply things out by hand you can get the answer.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
2K
Replies
9
Views
2K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
5
Views
2K