Linear algebra

Linear algebra

Linear algebra is a branch of a mathematics concepts in linear equations.  It will be representing matrices and vector spaces.

Linear algebra its a main area of all concepts in mathematics like a CPU of a computer.

Linear algebra is a feature representation 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. For nonlinear systems, which cannot be modeled with linear algebra, linear algebra is often used as a first-order approximation.

Vector spaces 

Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.

Matrices

Matrix (mathematics)

Matrices allow explicit manipulation of finite-dimensional vector spaces and linear maps. Their theory is thus an essential part of linear algebra.

Let V be a finite-dimensional vector space over a field F, and (v1, v2, ..., vm) be a basis of V (thus m is the dimension of V). By definition of a basis.

  
Pearson best fourth edition for linear  algebra and really value for money but customer rating is 5 out of 3.5 . my suggestion is pearson fourth edition for linear algebra not for the beginners for intermediate.

  

If  your a masters in a linear algebra the definitely you need to choose this author book it will help you for better learning methodology. The author name is Stephen H. friedberg

  
If your a beginner definitely my suggestion is schaum's outline third edition.it will complete beginner guide with 500 solved questions and answers.