Matrix Multiplication: Calculating (AB)C and A(BC) Using the Formula

Click For Summary
To calculate ((AB)C) and (A(BC)), start by applying the matrix multiplication formula (AB)ij = Pk AikBkj. For ((AB)C)ij, use the expression ((AB)C)ij = ∑k (AB)ik Ckj. Then, substitute (AB)ik with the formula to evaluate it further. Similarly, for (A(BC)), apply the formula to first compute (BC) and then multiply by A. This method ensures accurate computation of both expressions using the defined matrix multiplication rules.
P-Jay1
Messages
32
Reaction score
0
A is an M × N matrix, B is N × K and C is a K × L matrix. Consider matrix
multiplication (AB)ij = Pk AikBkj .

Using the formula, (AB)ij = Pk AikBkj, how would I calculate ((AB)C) and (A(BC))?
 
Physics news on Phys.org
P-Jay1 said:
A is an M × N matrix, B is N × K and C is a K × L matrix. Consider matrix
multiplication (AB)ij = Pk AikBkj .

Using the formula, (AB)ij = Pk AikBkj, how would I calculate ((AB)C) and (A(BC))?
Just use the formula twice (on each of those products). Start with ((AB)C)_{ij}=\sum_k(AB)_{ik}C_{kj}. Now use the formula again to evaluate (AB)_{ik}.
 

Thread 'Confusion about the Moyal-Weyl twist'

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...
View full post »

Similar threads

Undergrad The way matrices are written without boxes
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
  • · Replies 33 ·
2
Replies
33
Views
2K
Graduate Matrix multiplication, Orthogonal matrix, Independent parameters
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Index notation of vector rotation
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Explanation of a Line of a proof in Axler Linear Algebra Done Right 3r
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
  • · Replies 12 ·
Replies
12
Views
5K
Undergrad Solving matrix commutator equations?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Why is the dot product equivalent to matrix multiplication?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K