Course Of Linear Algebra And Multidimensional Geometry

Livro digital

Título:
Course Of Linear Algebra And Multidimensional Geometry

Autor:
Ruslan Sharipov

Categoria:
Matemática & Lógica > Álgebra e Teoria dos Números

Pessoa doadora:
Raffaello D. N.

Sinopse:
This textbook opens with sets, mappings, and the language of abstract linear vector spaces, then moves through linear dependence, bases, coordinates, and subspaces before reaching linear mappings and their matrices. The table of contents makes the progression explicit: from foundations in Chapter I to operators, dual spaces, bilinear and quadratic forms, Euclidean spaces, and affine spaces. The structure is strongly geometric as well as algebraic. Later chapters cover invariant subspaces, eigenvalues, nilpotent and Jordan theory, dual spaces and covectors, canonical forms of quadratic forms, orthogonality, selfadjoint operators, and Euclidean point spaces with quadrics. The preface emphasizes that the book follows an invariant geometric approach rather than a coordinates-first treatment. Readers get a compact, systematic path through core linear algebra and multidimensional geometry, with a textbook tone and a clear university-course scope. The result is a rigorous introduction that connects basic algebraic tools to the geometric ideas that support more advanced mathematics.