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공학 >기계ㆍ금속 >기계공학
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2013년 2학기

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Systems of linear Equations, Matrix Algebra, Euclidean Vector Space, Eigenvalues and Eigenvectors

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Systems of linear equations

차시별 강의

1.	Systems of linear equations	definition of vector, algebraic structures of vector space
	Systems of linear equations	pivots, ranks, free variables, augmented matrix, Gaussian elimination
2.	Systems of linear equations	Gauss-Jordan elimination
	Systems of linear equations	existence and uniqueness of systems of linear equations, floating-point number,partial pivoting,ill- conditioned system
3.	matrix multiplication, matrix inverse	full column rank, full row rank, left inverse, right inverse, two-sided inverse
4.	matrix multiplication, matrix inverse	one-to-one (injective) mapping, onto(surjective) mapping, bijective mapping, Fredholm alternative
	matrix multiplication, matrix inverse	Gauss-Jordan elimination by block matrics, Sherman_Morrison_Woodbury formula
5.	vector space	span,linear dependent and independent, basis, dimensions, transition matrix (changes of basis)
	vector space	column space, basic columns, full rank factorization, Vandemonde matrices
6.	determinants	permutations, transpositions, parity, minors, cofactors, determinant of triangular matrices
7.	determinants	Cramer's rule,determinants calculation by block matrices
	determinants, cross products	cross product, Vandermonde determinant
8.	Linear transformation	More about rank, Linear transformation
	Linear transformation	Linear transformation, Adjoint operator
9.	Linear transformation	Transposed matrix, Symmetric matrix, self-adjoint-operator
	Linear transformation	Four fundamental subspaces
10.	Inner product space	orthogonal projection,Gram Schmidt algorithm, QR decomposition, revised Gram Schmidt algorithm
	Inner product space	overdetermined systems, method of least squares, underdetermined system, minimum norm problems
11.	Eigenvalue problems	eigenvalues, eigenvectors, characteristic polynomials, characteristic equations
	Eigenvalue problems	Spectral theorem, Cayley-Hamilton theorem, Self-adjoint operators, Unitary operator, Hermitian operators
12.	Eigenvalue problems	Sylvesters formula, difference equations, Fibonacci numbers, dfferential equations
	Eigenvalue problems	Differential Equations (Boundary value problems), Toeplitz matrices, Tridiagonal matrices, Boundary Conditions
13.	Eigenvalue problems	Normal Modes of Oscillation, Bilinear Forms, Quadratic Forms, Quadratic Equations, Conic Sections, Positive Definite Forms
	Singular Value Decomposition	SVD (Singular Value Decomposition), Pseudoinverse, Algebraic Multiplicity, Geometric Mulitiplicity