# 吴军《数学之美》：数学模型帮您实现认知跨越

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# The ‘Useless’ Perspective That Transformed Mathematics | Quanta Magazine

https://www.quantamagazine.org/the-useless-perspective-that-transformed-mathematics-20200609/

“Representation” is the concretization / visualization of Abstract Math,
eg.
“Group Representation Theory” 群表示论 using Matrix (Linear Algebra).

Reference:

Artin’s Algebra book with matrix representation, lectured by Harvard Dean Prof Gross :

# An “Introduction of Introduction” to Category Theory

Category : 范畴 has 3 things: (hence richer than a Set 集合 which is only a collection of objects)

1. Objects 对象
2. Arrow (Morphism 态射) between Objects, includes identity morphism.
3. Associativity 结合性

Functor (函子) between 2 Categories (preserve structure)

Natural Transformation 自然变换

• Example :
Matrices -> Determinants

..

# Matrix A.X = 0

1) Row reduction, row-echelon form and reduced row-echelon form

2) Rank of Matrix = Rank (A)

# Darcy Lecture 5 ~ 9: Applied Algebraic Topology

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)

# Matrix Tensor Product

Note the difference from Matrix Multiplication:

# Quicker Way to Inverse 3×3 Matrix

This is a quick method to inverse a matrix using the analogy of determinant:

# Sylvester, Matrix, Nightingale

Sylvester, James Joseph
(1841-1897)
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.