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Linear Algebra, Geometry and Transformation
I have been writing about linear algebra almost non-stop for the past two months to organize the best possible "playlist" of topics that cover a linear algebra course. It's a hard problem, this linearization of a graph of dependencies into a stream of. Simoncelli has a very good geometrical take on the problem. He manages to cover all the essential topics in 10 pages. All the essential topics? I miss eigenvalues and probably determinants as a stepping stone to that.
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Linear algebra is the branch of mathematics concerning linear equations such as. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry , including for defining basic objects such as lines , planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models.
This book on linear algebra and geometry is based on a course given by renowned academician I. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics in affine and projective spaces , decomposition of finite abelian groups, and finitely generated periodic modules similar to Jordan normal forms of linear operators. Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics. Skip to main content Skip to table of contents. Advertisement Hide.