Engineering Math

18년 1학기에 서울시립대학교에서 수강했던 Engineering Math를 제 필요에 의해 정리해봅니다. 영어 강의이고 제가 다시 참고하기 위한 글입니다. 귀찮은 부분 다 건너 뛰어요.

Matrix

  • : collection of numbers. i: row, j: col

  • 에서 1~4 방향이 col, 4~6 방향이 row. 그리고 각각이 element.

  • : 2x3 matrix (#row x #col matrix)

연산

Transpose

.

associative: , .

Multiplication

In general, . -> matrix multiplication is non commutative. “Non-Abelian”1

Determinant

for 2x2 matrix

if , then

for larger matrix

프로그래머를-위한-선형대수1-벡터,행렬,행렬식 포스트 참고

Inverse

,

(if )

Eigen value problem

  • : eigen value problem

  • : eigen vector
  • : eigen value

.

Hermitian matrix

A matrix is the hermitian matrix if ( = complex conjugate) 2

norm

, : inner product

called norm of a vector

normalized vector

: normalized vector

,

Eigen value problem

  1. : : null vector
  2. then we have an arbitrary solution.
  • we will be focusing on the “Hermitian matrix” only

Other matrices

Identity matrix

. Identity matrix I plays the same role as the number 1 in the multiplication of numbers.

Square matrix

  • square matrix: nxn matrix
  • closed to addition, subtraction and multiplication

Example : 3

Column, Row Vector

: column vector (column matrix) or ket vector4

: row vector (row matrix) or bra vector4

braket notation

.

Pauli matrix

Differential equation

Ordinary Differential Equation O.D.E.

Partial Differential Equation P.D.E.

Exact & Separable

O.D.E.

Integrating Factor

Homogeneous & Inhomogeneous

Equidimensional O.D.E.

Inhomogen

  1. https://en.wikipedia.org/wiki/Non-abelian_group 

  2. https://en.wikipedia.org/wiki/Conjugate_transpose 수업에서는 dagger로 주로 쓰셨다. 

  3. https://en.wikipedia.org/wiki/Kronecker_delta 

  4. https://en.wikipedia.org/wiki/Bra–ket_notation  2

August 22, 2018 에 작성
Tags: engineering math 대학