Exploring Non-Commutative Matrices with Symmetry: Can We Break the Rules?

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In summary, the conversation discusses the concept of matrices not being commutative and explores various scenarios where this property may not hold true. The conversation also mentions the possibility of creating new matrices by adding or multiplying existing ones, and poses a question about creating additional examples of non-commutative matrices.
  • #1
brandy
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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?
 
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  • #2
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.
 
  • #3
Both A and B symmetric.
 

What is rebelious matrix commutivity?

Rebelious matrix commutivity is a term used in mathematics to describe the behavior of certain matrices when they are multiplied together. It refers to the fact that the order in which the matrices are multiplied can affect the result.

Why is rebelious matrix commutivity important in mathematics?

Rebelious matrix commutivity is important because it can affect the accuracy of calculations and solutions in mathematical models and equations. It is important for scientists and mathematicians to be aware of this behavior in order to accurately interpret and analyze data.

How does rebelious matrix commutivity differ from traditional matrix multiplication?

In traditional matrix multiplication, the order of the matrices does not affect the result. However, in rebelious matrix commutivity, the order of the matrices can change the result, making it a non-commutative operation.

What are some real-world applications of rebelious matrix commutivity?

Rebelious matrix commutivity can be seen in various fields such as physics, economics, and computer science. It plays a crucial role in quantum mechanics, financial modeling, and cryptography, among others.

Are there any strategies to deal with rebelious matrix commutivity?

There are various strategies to deal with rebelious matrix commutivity, such as using different matrix multiplication algorithms or rearranging the matrices in a specific order to achieve the desired result. It is also important to carefully consider the order in which matrices are multiplied when working with data that may exhibit this behavior.

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