Matrix Multiplication Explained: Why & What's the Pro?

Click For Summary
SUMMARY

The discussion centers on the mathematical principles of matrix multiplication, specifically addressing the multiplication of a matrix A with a column matrix C and a diagonal matrix D. The formula AC = C1A1 + C2A2 + ... + CnAn is established as a foundational concept. Participants are encouraged to refer to their textbooks for the formal definitions of the product of matrices A_{(p,r)} and D_{(r,q)} to deepen their understanding of these operations.

PREREQUISITES
  • Understanding of matrix notation and operations
  • Familiarity with diagonal matrices
  • Basic knowledge of linear algebra concepts
  • Access to a linear algebra textbook for definitions
NEXT STEPS
  • Review the definition of matrix multiplication in linear algebra textbooks
  • Study the properties of diagonal matrices and their impact on multiplication
  • Explore vector products and their applications in matrix operations
  • Practice matrix multiplication problems to reinforce understanding
USEFUL FOR

Students studying linear algebra, mathematics enthusiasts, and anyone seeking to understand the principles of matrix multiplication and its applications.

jugalyash
Messages
3
Reaction score
0
if A is [A1|A2|A3|...|An] and C is 1 column matrix given by [C1|C2|C3|...|Cn]T then AC=C1A1+C2A2+...+CnAn.. If D is a diagonal matrix then AD = [D11A1+D22A2+...+DNnAn]. please explain why it happens tht way and whts the prof?
 
Physics news on Phys.org
The first rule you state is true but only tells you about the product of vectors. Do you know the definition for the product for A_{(p,r)} and D_{(r,q)}? Find the definition in your textbook and give it a try and post us what you did.

This should be in the homework forum!
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
4K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
7K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K