LaTeX
(AB)_{ij}=\sum_k A_{ik}B_{kj}Variables
- A,B: compatible matrices
- i,j,k: indices
How to use this formula
Defines each entry of a matrix product.
Important notes
- Inner dimensions must match.
Quick example
A 2×3 matrix can multiply a 3×4 matrix.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Inner dimensions must match.
- For the Matrix Multiplication, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- Matrix and vector dimensions must be compatible, and any required inverse, determinant, rank, or basis condition must hold.
Worked example
A 2×3 matrix can multiply a 3×4 matrix.
Common mistakes
- Do not omit the index or bounds in Matrix Multiplication; changing either one changes which terms are included.
- Do not assume commutativity, invertibility, independence, or full rank unless the required condition has been established.
Continue the workflow
Use Matrix Multiplication in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
(AB)_{ij}=\sum_k A_{ik}B_{kj}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Matrix Multiplication used for?
Defines each entry of a matrix product.
Can I copy this formula as LaTeX?
Yes. Copy (AB)_{ij}=\sum_k A_{ik}B_{kj} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.