Linear (Vector) Space
2026TheorySergey
The axioms of a linear (vector) space, examples and counterexamples.
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160
Search results for “algebra”
Categories
50 results
Basis, Dimension, and Span
2026TheorySergey
Linear dependence of vectors, basis and coordinates, dimension, subspaces, and linear span.
0
220
Linear Operator
2026TheorySergey
A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.
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150
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
A non-Noetherian local ring with finitely generated maximal ideal
2026NotesBogdan Zavyalov
A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.
0
340