- Solve linear algebra equations in several ways
- Put data in order with matrices
- Determine values with determinants
- Work with eigenvalues and eigenvectors
Your hands-on guide to real-world applications of linear algebra
Does linear algebra leave you feeling lost? No worries this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction.
- Line up the basics discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
- Relate vectors and linear transformations link vectors and matrices with linear combinations and seek solutions of homogeneous systems
- Evaluate determinants see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule
- Hone your skills with vector spaces determine the properties of vector spaces and their subspaces and see linear transformation in action
- Tackle eigenvalues and eigenvectors define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices
Open the book and find:
- Theoretical and practical ways of solving linear algebra problems
- Definitions of terms throughout and in the glossary
- New ways of looking at operations
- How linear algebra ties together vectors, matrices, determinants, and linear transformations
- Ten common mathematical representations of Greek letters
- Real-world applications of matrices and determinants
Part I: Lining Up the Basics of Linear Algebra.
Chapter 1: Putting a Name to Linear Algebra.
Chapter 2: The Value of Involving Vectors.
Chapter 3: Mastering Matrices and Matrix Algebra.
Chapter 4: Getting Systematic with Systems of Equations.
Part II: Relating Vectors and Linear Transformations.
Chapter 5: Lining Up Linear Combinations.
Chapter 6: Investigating the Matrix Equation Ax = b.
Chapter 7: Homing In on Homogeneous Systems and Linear Independence.
Chapter 8: Making Changes with Linear Transformations.
Part III: Evaluating Determinants.
Chapter 9: Keeping Things in Order with Permutations.
Chapter 10: Evaluating Determinants.
Chapter 11: Personalizing the Properties of Determinants.
Chapter 12: Taking Advantage of Cramer’s Rule.
Part IV: Involving Vector Spaces.
Chapter 13: Involving Vector Spaces.
Chapter 14: Seeking Out Subspaces of Vector Spaces.
Chapter 15: Scoring Big with Vector Space Bases.
Chapter 16: Eyeing Eigenvalues and Eigenvectors.
Part V: The Part of Tens.
Chapter 17: Ten Real-World Applications Using Matrices.
Chapter 18: Ten (Or So) Linear Algebra Processes You Can Do on Your Calculator.
Chapter 19: Ten Mathematical Meanings of Greek Letters.