Γραμμική Άλγεβρα
| Code | 9.2.3132.1 |
|---|---|
| Semester | 1st |
| Category | |
| Credits | 5 |
| Class Hours - Lab Hours | 4 - 0 |
| Lecturers | Panagiotis Psarrakos, Kalliopi Pavlopoulou |
| Links | Helios |
| Web Platform |
Class 1:
Webex
|
Description
Matrices, matrix operations, inverse matrix. Determinants, properties of determinants, computation of inverse matrix. Systems of linear equations, echelon form, Gauss' elimination, matrix rank, Cramer's rule. Vector spaces and subspaces, sum and intersection of vector subspaces, linear dependent and independent sets, bases and dimension of a vector space, the dimension theorem. Linear maps, the matrix of a linear map, image and null space of a linear map, change of basis, similar matrices. Inner product vector spaces, orthogonal bases, orthogonal complement. Eigenvalues and eigenvectors of matrices, the characteristic polynomial of a matrix, diagonalization of matrices, the theorem of Cayley-Hamilton, the minimum polynomial of a matrix. Vector calculus, lines and planes in space, surfaces and curves in space, cylindrical and conical surfaces, surfaces of revolution, surfaces of second degree.