Algebra Lineare E Geometria Bottacin Pdf 49: A Comprehensive Guide
If you are looking for a book that covers the topics of linear algebra and geometry in a clear and rigorous way, you might want to check out Algebra Lineare E Geometria by Francesco Bottacin. This book is based on the lectures given by the author at the University of Padua, Italy, and it is suitable for students of engineering, computer science, physics, and mathematics. In this article, we will give you an overview of the book's contents, features, and benefits, as well as some tips on how to download it for free.
What is Algebra Lineare E Geometria
Algebra Lineare E Geometria is a book that covers the basic concepts and methods of linear algebra and geometry, with an emphasis on applications and examples. The book consists of 10 chapters, each divided into sections and subsections. The chapters are:
Chapter 1: Algebraic structures. This chapter introduces the notions of sets, operations, groups, rings, fields, and vector spaces.
Chapter 2: Linear spaces. This chapter deals with linear combinations, linear independence, bases, dimension, subspaces, intersection, sum, and Grassmann's formula.
Chapter 3: Linear maps and matrices. This chapter defines linear maps, matrices, matrix operations, matrix representation of linear maps, composition, inverse, determinant, Laplace's formula, elementary operations, triangular form, echelon form, rank.
Chapter 4: Systems of linear equations. This chapter explains how to solve systems of linear equations using Cramer's theorem, RouchÃ-Capelli theorem, Gaussian elimination method. It also discusses homogeneous and non-homogeneous systems and their relation to the kernel and image of a linear map.
Chapter 5: Eigenvalues and eigenvectors. This chapter introduces the concepts of eigenvalues and eigenvectors of a linear map or a matrix. It also defines the characteristic polynomial and equation, eigenspaces, diagonalization.
Chapter 6: Euclidean spaces. This chapter introduces the notions of inner product, norm, distance, angle, orthogonality. It also discusses orthogonal bases, Gram-Schmidt process, orthogonal projection.
Chapter 7: Linear transformations in Euclidean spaces. This chapter studies the properties of linear transformations in Euclidean spaces such as symmetry,
Linear transformations in Euclidean spaces
This chapter studies the properties of linear transformations in Euclidean spaces such as symmetry, orthogonality, isometry, rotation, reflection, scaling. It also defines the matrix of a linear transformation with respect to an orthogonal basis, the adjoint of a linear map, the spectral theorem for symmetric matrices.
Affine spaces and Euclidean geometry
This chapter introduces the concepts of affine spaces, affine maps, affine combinations, barycentric coordinates. It also discusses Euclidean geometry in affine spaces, such as lines, planes, parallelism, perpendicularity, angles, triangles, circles.
Complex numbers and matrices
This chapter reviews the properties of complex numbers and their geometric interpretation. It also defines complex matrices and vectors, complex linear maps and spaces, Hermitian inner product, unitary matrices and maps.
Conics and quadrics
This chapter studies the classification and properties of conics and quadrics in affine and Euclidean spaces. It also defines the matrix of a conic or a quadric with respect to a suitable basis, the canonical forms of conics and quadrics. ec8f644aee