Introduction to Linear Algebra (Chapter1)

Chapter 1 introduce to Vectors

Two core operations of linear algebra: vector addition and multiplication. Combining these two operations is a linear combination of vectors.

1.1 Vector and Linear combinations

Two basic operations: vector addition and multiplication.

two x vector v and W linear combination of : Cv+aw. where C and a are arbitrary scalars.

1.2 Lengths and Dot products

dot product : The inner product of a vector. ------------- in relation to length and angle, the "geometry" part of linear algebra

orthogonal : vector dot product is 0, angle is 90 degrees

vector length : sqrt (the vector and its own dot product).

the angle between two vectors : inner product/length.

Cauchy inequality : The product of the vector inner product is less than or equal to the length of the vector. ----------the most important inequalities in mathematics

1.3 matrices

A*x is considered as a linear combination of the column spaces of a.

differential matrices : forward differential and back differential. The difference is a constant compared to the differential.

Inverse of the matrix.

Independence and correlation between vectors

Introduction to Linear Algebra (Chapter1)