강의노트, 강의정리 - Kreyszig: Linear Algebra, Vector Calculus: Matrix

Linear Algebra - Matrix

Lecture 4. Matrix simplified

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matrix, entries,
transpose matrix, symmetric matrix, orthogonal matrix,
matrix multiplication,
trace, determinant, minors, co-factors, adj A, A inverse,
characteristic polynomial, Cayley Hamilton theorem,
cramer's rule
** polynomial과 matrix 연결 : Cayley Hamilton theorem
    Cayley Hamilton theorem의 의미 : 대수학에서 function을 분해 하였고,
                                                   vector도 basis로 분해하였고,
                                                   matrix도 C.H. theorem로 분해.

Lecture 5. more about Matrices 1/2

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determinant calculation,
some facts about determinant
similarity transformation of A, B=inv T*A*T: so what?, 어디써?

Lecture 6. more about Matrices 2/2

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** think about Matrix as a vector transformer (수업 중 다루었던 내용)
eigenvalue, eigenvectors
eigenvalue, eigenvector and geometrical relation: transform과 연관하여 좀더 심도있게 공부
A*T=T*L -> inv T*A*T=L, (A: given matrix, T: e.vector 모음, L: e. value 모음)

Function of matrix

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invertible matrix (non-singular matrix)