Inverse Matrices
2026TheorySergey
Nonsingular matrices, the invertibility criterion, the adjugate-matrix formula, and the Gauss–Jordan method.
0
120
Search results for “LIME”
102 results
Matrix Rank
2026TheorySergey
Minors and the rank of a matrix, invariance of rank under elementary transformations, and a practical method for computing it.
0
190
Cramer's Rule and Gaussian Elimination
2026TheorySergey
Two methods for solving a SLAE — Cramer's rule via determinants and the universal Gaussian elimination method, with examples.
0
250
Eigenvectors and Eigenvalues
2026TheorySergey
Eigenvectors and eigenvalues, the characteristic equation, eigenspaces, and diagonalization of matrices.
0
170
Change of Basis
2026TheorySergey
The change-of-basis matrix, recomputing a vector's coordinates and an operator's matrix, and the orthonormal case.
0
220
Quadratic Forms
2026TheorySergey
Quadratic forms and their matrix, definiteness, Sylvester's criterion, and canonical form.
0
160
Vector calculus. Surface integrals of the first kind
2026Problem sheetSergey
Integration with respect to surface area: the area element for an explicit and a parametric surface, pieces of planes, the sphere in spherical coordinates.
0
340
Vector calculus. Surface integrals of the second kind. Flux
2026Problem sheetSergey
The flux of a vector field through an oriented surface: the normal and the choice of side, the explicit and parametric forms, the lateral surface of a cylinder.
0
380
Vector calculus. Stokes' theorem. Circulation
2026Problem sheetSergey
Circulation of a field as the flux of its curl: computing the curl, matching the orientation of the contour and the normal, circulation computed two ways.
0
310