What is the theory behind elementary matrices?

Click For Summary
Elementary matrices are defined as matrices in the form E(σ, u, v) = I - (1/σ)uv^T, where I is the identity matrix. They play a crucial role in linear algebra, particularly in operations like row reduction and transformations. Resources on elementary matrices can typically be found in standard linear algebra textbooks, which cover their properties and applications. The discussion highlights a lack of specific online resources for this topic. Understanding elementary matrices is essential for grasping more complex concepts in linear algebra.
stanley.st
Messages
30
Reaction score
0
Hello,

I need to find some theory about elementary matrices. That are the matrices in the form

\mathbf{E}(\sigma,\mathbf{u},\mathbf{v})=\mathbf{I}-\frac{1}{\sigma}\mathbf{uv}^{T}

I can't find anywhere some theory about it. Can you give me some useful links?

Thank you so much...
 
Mathematics news on Phys.org
Hello stanley.st! :smile:

If you can't find a link, where did you come across this?

(it's not something I've seen before)
 
Any decent linear algebra book covers elementary matrices.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Deriving Bogoliubov transformations correctly
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad What should I say about elementary number theory?
  • · Replies 2 ·
Replies
2
Views
1K
MHB What should I say about elementary number theory?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Instantaneous electric field solved by extended electrodynamics?
  • · Replies 1 ·
Replies
1
Views
503
Magnetic Field of Uniformly Magnetized Infinite Slab
  • · Replies 6 ·
Replies
6
Views
2K
Graduate How to show spin ##= \pm 2/\omega## for a circ-polarized gravity wave
  • · Replies 0 ·
Replies
0
Views
1K
Coordinate Transformation (multivariable calculus)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why Must Pure Force Depend on 4-Velocity?
  • · Replies 47 ·
2
Replies
47
Views
5K
Graduate Synchronous to Newtonian gauge
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Electric and magnetic field lines in a plane wave of finite extent
  • · Replies 1 ·
Replies
1
Views
1K