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Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models.

With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.

This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION

Recognizing Linear Systems and Solutions

Matrices, Equivalence and Row Operations

Echelon Forms and Gaussian Elimination

Free Variables and General Solutions

The Vector Form of the General Solution

Geometric Vectors and Linear Functions

Polynomial Interpolation

MATRIX NUMBER SYSTEMS

Complex Numbers

Matrix Multiplication

Auxiliary Matrices and Matrix Inverses

Symmetric Projectors, Resolving Vectors

Least Squares Approximation

Changing Plane Coordinates

The Fast Fourier Transform and the Euclidean Algorithm.

DIAGONALIZABLE MATRICES

Eigenvectors and Eigenvalues

The Minimal Polynomial Algorithm

Linear Recurrence Relations

Properties of the Minimal Polynomial

The Sequence {Ak}

Discrete dynamical systems

Matrix compression with components

DETERMINANTS

Area and Composition of Linear Functions

Computing Determinants

Fundamental Properties of Determinants

Further Applications

Appendix: The abstract setting

Selected practice problem answers

Index

Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models.

With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.

This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION

Recognizing Linear Systems and Solutions

Matrices, Equivalence and Row Operations

Echelon Forms and Gaussian Elimination

Free Variables and General Solutions

The Vector Form of the General Solution

Geometric Vectors and Linear Functions

Polynomial Interpolation

MATRIX NUMBER SYSTEMS

Complex Numbers

Matrix Multiplication

Auxiliary Matrices and Matrix Inverses

Symmetric Projectors, Resolving Vectors

Least Squares Approximation

Changing Plane Coordinates

The Fast Fourier Transform and the Euclidean Algorithm.

DIAGONALIZABLE MATRICES

Eigenvectors and Eigenvalues

The Minimal Polynomial Algorithm

Linear Recurrence Relations

Properties of the Minimal Polynomial

The Sequence {Ak}

Discrete dynamical systems

Matrix compression with components

DETERMINANTS

Area and Composition of Linear Functions

Computing Determinants

Fundamental Properties of Determinants

Further Applications

Appendix: The abstract setting

Selected practice problem answers

Index

Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models.

With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.

This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION

Recognizing Linear Systems and Solutions

Matrices, Equivalence and Row Operations

Echelon Forms and Gaussian Elimination

Free Variables and General Solutions

The Vector Form of the General Solution

Geometric Vectors and Linear Functions

Polynomial Interpolation

MATRIX NUMBER SYSTEMS

Complex Numbers

Matrix Multiplication

Auxiliary Matrices and Matrix Inverses

Symmetric Projectors, Resolving Vectors

Least Squares Approximation

Changing Plane Coordinates

The Fast Fourier Transform and the Euclidean Algorithm.

DIAGONALIZABLE MATRICES

Eigenvectors and Eigenvalues

The Minimal Polynomial Algorithm

Linear Recurrence Relations

Properties of the Minimal Polynomial

The Sequence {Ak}

Discrete dynamical systems

Matrix compression with components

DETERMINANTS

Area and Composition of Linear Functions

Computing Determinants

Fundamental Properties of Determinants

Further Applications

Appendix: The abstract setting

Selected practice problem answers

Index

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION

Recognizing Linear Systems and Solutions

Matrices, Equivalence and Row Operations

Echelon Forms and Gaussian Elimination

Free Variables and General Solutions

The Vector Form of the General Solution

Geometric Vectors and Linear Functions

Polynomial Interpolation

MATRIX NUMBER SYSTEMS

Complex Numbers

Matrix Multiplication

Auxiliary Matrices and Matrix Inverses

Symmetric Projectors, Resolving Vectors

Least Squares Approximation

Changing Plane Coordinates

The Fast Fourier Transform and the Euclidean Algorithm.

DIAGONALIZABLE MATRICES

Eigenvectors and Eigenvalues

The Minimal Polynomial Algorithm

Linear Recurrence Relations

Properties of the Minimal Polynomial

The Sequence {Ak}

Discrete dynamical systems

Matrix compression with components

DETERMINANTS

Area and Composition of Linear Functions

Computing Determinants

Fundamental Properties of Determinants

Further Applications

Appendix: The abstract setting

Selected practice problem answers

Index

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION

Recognizing Linear Systems and Solutions

Matrices, Equivalence and Row Operations

Echelon Forms and Gaussian Elimination

Free Variables and General Solutions

The Vector Form of the General Solution

Geometric Vectors and Linear Functions

Polynomial Interpolation

MATRIX NUMBER SYSTEMS

Complex Numbers

Matrix Multiplication

Auxiliary Matrices and Matrix Inverses

Symmetric Projectors, Resolving Vectors

Least Squares Approximation

Changing Plane Coordinates

The Fast Fourier Transform and the Euclidean Algorithm.

DIAGONALIZABLE MATRICES

Eigenvectors and Eigenvalues

The Minimal Polynomial Algorithm

Linear Recurrence Relations

Properties of the Minimal Polynomial

The Sequence {Ak}

Discrete dynamical systems

Matrix compression with components

DETERMINANTS

Area and Composition of Linear Functions

Computing Determinants

Fundamental Properties of Determinants

Further Applications

Appendix: The abstract setting

Selected practice problem answers

Index

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION

Recognizing Linear Systems and Solutions

Matrices, Equivalence and Row Operations

Echelon Forms and Gaussian Elimination

Free Variables and General Solutions

The Vector Form of the General Solution

Geometric Vectors and Linear Functions

Polynomial Interpolation

MATRIX NUMBER SYSTEMS

Complex Numbers

Matrix Multiplication

Auxiliary Matrices and Matrix Inverses

Symmetric Projectors, Resolving Vectors

Least Squares Approximation

Changing Plane Coordinates

The Fast Fourier Transform and the Euclidean Algorithm.

DIAGONALIZABLE MATRICES

Eigenvectors and Eigenvalues

The Minimal Polynomial Algorithm

Linear Recurrence Relations

Properties of the Minimal Polynomial

The Sequence {Ak}

Discrete dynamical systems

Matrix compression with components

DETERMINANTS

Area and Composition of Linear Functions

Computing Determinants

Fundamental Properties of Determinants

Further Applications

Appendix: The abstract setting

Selected practice problem answers

Index