“Representation” is the concretization / visualization of Abstract Math,
“Group Representation Theory” 群表示论 using Matrix (Linear Algebra).
Artin’s Algebra book with matrix representation, lectured by Harvard Dean Prof Gross :
Data Science & Machine Learning (AI is a sub-discipline) overlap but not the same:
Category : 范畴 has 3 things: (hence richer than a Set 集合 which is only a collection of objects)
- Objects 对象
- Arrow (Morphism 态射) between Objects, includes identity morphism.
- Associativity 结合性
Functor (函子) between 2 Categories (preserve structure)
Natural Transformation 自然变换
- Example :
Matrices -> Determinants
1) Row reduction, row-echelon form and reduced row-echelon form
2) Rank of Matrix = Rank (A)
[Revision – Lecture 1 ~4: Foundation of Applied Algebraic Topology
Lecture 6: Creating Simplicial Complex]
Lecture 5: 4/9/2013 (三) Clustering Via Persistent Homology
Lecture 7: 6/9/2013 (五) Calculating Homology using matrix
Lecture 8: Column Space and Null Space of a matrix
Lecture 9: 9/9/2013 (一) Create your own Homology: (Important lecture in Applied Algebraic Topology)
Note the difference from Matrix Multiplication:
This is a quick method to inverse a matrix using the analogy of determinant:
Sylvester, James Joseph
Cambridge, St John’s college. He coined the word ‘Matrix‘.
His private math tuition student was Florence Nightingale (Founder of Nursing), who later applied her statistics math in Nursing.