Can Non-Commutative Symmetric Matrices Defy Mathematical Rules?

  • Thread starter Thread starter brandy
  • Start date Start date
  • Tags Tags
    Matrix
AI Thread Summary
Non-commutative symmetric matrices challenge traditional mathematical rules, particularly regarding commutativity. The discussion explores scenarios where matrices may appear to defy these rules, such as when matrices are equal or involve identity and null matrices. The user seeks assistance in identifying additional examples, particularly when considering matrices of the form B = A + xI, where A and B are diagonal and symmetric. The exploration emphasizes the potential for unique cases that could lead to new insights in matrix theory. The conversation invites further contributions to expand on these intriguing mathematical concepts.
brandy
Messages
156
Reaction score
0
hey i was just thinking how matrices aren't supposed to be commutative?
well i was just thinking, what if the matricees were equal? and i was like ha! I am so cool! take that mr logic.
so yea, so far i have a couple rebelious matricees
a*b where a=1 by 1 and b= 1 by 1
a*b where na=b
a*b where a^n=b
a*b where a= identity
a*b where na=b and a = identity
a*b where a = null
a*b where a= mutliple of identity and b= multiple of mirrored identity

so, my questiono is this, can you help me be a good little poindexter and come up with a couple others?
 
Last edited:
Mathematics news on Phys.org
Consider what happens if B = A + xI (for some real number x, I being the identity matrix) and if A and B are diagonal matrices.
 
Both A and B symmetric.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Solving matrix commutator equations?
Replies
7
Views
3K
I Congruence for Symmetric and non-Symmetric Matrices for Quadratic Form
Replies
7
Views
2K
Solving Logistic ODE with Non-commuting Matrices
Replies
6
Views
2K
Can G be Written as a Matrix of Matrices like H?
Replies
1
Views
2K
MHB Find Matrix A: Determining Inverse of Matrices
Replies
2
Views
1K
What is a Group Representation and How Does it Act on a Vector Space?
Replies
1
Views
2K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
Replies
2
Views
1K
Prove the identity matrix is unique
2
Replies
69
Views
8K
What Are Symmetric Groups and Their Mathematical Significance?
Replies
1
Views
3K
Showing that real symmetric matrices are diagonalizable
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top