Akademik Dersler - İçerik

Is comfortable with basic matrix and vector definitions and operations like matrix addition, product, transpose, inner product of vectors etc.
Knows the concepts of linear equation system and Gauss-Jordan method.
Knows the concept of linear transformation and its types.
Understands the concept of matrix inverse and how to compute it by solving an equation system.
Understands the basic conceps of vector spaces: (i) Understands the definition of a vector space, linear independence/dependence of vectors, basis vectors, coordinate transformations. (ii) Understands the concepts of matrix rank, range and null space of a matrix and their bases.
Understands the concepts of orthogonality and least-squares: (i) Knows vector norm, orthogonality of vectors and vector spaces, orthogonal projection. (ii) Understands Gram-Schmidt orthogonalization and QR factorization. (iii) Knows basics of orthogonal matrices and transformations. (iv) Understands least-squares solutions of overdetermined systems of equations and their use in curve fitting.
Understands determinants with basic properties and physical interpretations, how to compute them by Laplace expansion, Cramer rule and computing inverse of a matrix by means of classical adjoint.
Understands eigenvalues, eigenvectors, characteristic equation, diagonalization and Cayley-Hamilton theorem.