Álgebra lineal – Fernando Barrera Mora
One of the most popular topics that have been written countless texts mathematics, is the linear algebra. This is no accident. Linear algebra appears naturally in virtually all disciplines, both
mathematics and other sciences, including social sciences and
humanities, with significant presence in the areas of engineering, let
alone physics.
From our early studies, say at secondary level, linear algebra is studied, although it is not used that name, for solving systems of linear equations.
Because of this, when a new text related to linear algebra appears on the market, one wonders what can contribute that has not been presented and studied ad nauseam in some of the countless texts that already exist.
The book of Fernando Barrera Mora is dedicated to linear algebra course for a first degree in mathematics, engineering and related areas. The first point I would like to note is that the book gives priority to start with concrete problems that we face both in our daily lives, as in economics, productive enterprises, and so on. From these specific problems you begin to elaborate on the ingredients present which make viewing the student on these components when they are raised in general.
In addition, these specific problems are studied serve to establish both the methods and the theory necessary either to solve them, study them or place them in a broader context.
A valuable point of view to highlight in this work is the treatment that is what we might call the "own theory", that is, the theory that deals with values and eigenvectors.
The most common approach the solution and study of values and eigenvectors is the study of the characteristic matrix, ie, find the values for which this matrix is singular, which leads immediately to the calculation of the determinant and therefore the characteristic polynomial.
Although the analysis of the determinants is essential in the study of linear algebra, to present a comprehensive study of its basic properties is a problem either laborious or unclear, depending on the approach you select.
In this paper a different path is selected. emphasis on inherent in the matrix that give rise to the problem under study is made properties. More precisely, the operator associated with the matrix, be another appropriately selected besides the natural advantage that has to study, inherently, the operator basis is studied. Thus, it must be introduced without any need to refer to the determinants done.
Content:
IntroductionNomenclature1. Systems of linear equations2. Matrices3. Vector Spaces4. Linear transformations and matrices5. Determinants6. Eigenteoría: structure operators7. inner product spacesBibliographyIndex
From our early studies, say at secondary level, linear algebra is studied, although it is not used that name, for solving systems of linear equations.
Because of this, when a new text related to linear algebra appears on the market, one wonders what can contribute that has not been presented and studied ad nauseam in some of the countless texts that already exist.
The book of Fernando Barrera Mora is dedicated to linear algebra course for a first degree in mathematics, engineering and related areas. The first point I would like to note is that the book gives priority to start with concrete problems that we face both in our daily lives, as in economics, productive enterprises, and so on. From these specific problems you begin to elaborate on the ingredients present which make viewing the student on these components when they are raised in general.
In addition, these specific problems are studied serve to establish both the methods and the theory necessary either to solve them, study them or place them in a broader context.
A valuable point of view to highlight in this work is the treatment that is what we might call the "own theory", that is, the theory that deals with values and eigenvectors.
The most common approach the solution and study of values and eigenvectors is the study of the characteristic matrix, ie, find the values for which this matrix is singular, which leads immediately to the calculation of the determinant and therefore the characteristic polynomial.
Although the analysis of the determinants is essential in the study of linear algebra, to present a comprehensive study of its basic properties is a problem either laborious or unclear, depending on the approach you select.
In this paper a different path is selected. emphasis on inherent in the matrix that give rise to the problem under study is made properties. More precisely, the operator associated with the matrix, be another appropriately selected besides the natural advantage that has to study, inherently, the operator basis is studied. Thus, it must be introduced without any need to refer to the determinants done.
Content:
IntroductionNomenclature1. Systems of linear equations2. Matrices3. Vector Spaces4. Linear transformations and matrices5. Determinants6. Eigenteoría: structure operators7. inner product spacesBibliographyIndex
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