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Linear Algebra For Dummies
Making the Right Moves with Orthogonal Bases .....................................279
Creating an orthogonal basis ...........................................................281
Using the orthogonal basis to write the linear combination .......282
Making orthogonal orthonormal......................................................283
Writing the Same Vector after Changing Bases .......................................285
Chapter 16: Eyeing Eigenvalues and Eigenvectors . . . . . . . . . . . . . . .289
Defining Eigenvalues and Eigenvectors ....................................................289
Demonstrating eigenvectors of a matrix.........................................290
Coming to grips with the eigenvector definition ...........................291
Illustrating eigenvectors with reflections and rotations ..............291
Solving for Eigenvalues and Eigenvectors ................................................294
Determining the eigenvalues of a 2 × 2 matrix ...............................294
Getting in deep with a 3 × 3 matrix ..................................................297
Circling Around Special Circumstances ...................................................299
Transforming eigenvalues of a matrix transpose ..........................300
Reciprocating with the eigenvalue reciprocal ...............................301
Triangulating with triangular matrices ...........................................302
Powering up powers of matrices .....................................................303
Getting It Straight with Diagonalization ....................................................304
Part V: The Part of Tens ............................................ 309
Chapter 17: Ten Real-World Applications Using Matrices . . . . . . . .311
Eating Right ..................................................................................................311
Controlling Traffic .......................................................................................312
Catching Up with Predator-Prey ................................................................314
Creating a Secret Message ..........................................................................315
Saving the Spotted Owl ...............................................................................317
Migrating Populations .................................................................................318
Plotting Genetic Code .................................................................................318
Distributing the Heat ...................................................................................320
Making Economical Plans ...........................................................................321
Playing Games with Matrices .....................................................................322
Chapter 18: Ten (Or So) Linear Algebra Processes
You Can Do on Your Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327
Letting the Graph of Lines Solve a System of Equations ........................328
Making the Most of Matrices ......................................................................329
Adding and subtracting matrices ....................................................330
Multiplying by a scalar ......................................................................330
Multiplying two matrices together ..................................................330