Preface


This is a tutorial made solely for the purpose of education and it was designed for students taking Applied Math 0340. It is primarily for students who have some experience using Mathematica. If you have never used Mathematica before and would like to learn more of the basics for this computer algebra system, it is strongly recommended looking at the APMA 0330 tutorial. As a friendly reminder, don'r forget to clear variables in use and/or the kernel.

Finally, the commands in this tutorial are all written in bold black font, while Mathematica output is in normal font. This means that you can copy and paste all commands into Mathematica, change the parameters and run them. You, as the user, are free to use the scripts for your needs to learn the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately.

Return to computing page for the first course APMA0330
Return to computing page for the second course APMA0340
Return to Mathematica tutorial for the first course APMA0330
Return to Mathematica tutorial for the second course APMA0340
Return to the main page for the course APMA0340
Return to the main page for the course APMA0330
Return to Part IV of the course APMA0340

Generalized Eigenvectors


A = {{1, 1, 1}, {-1, 1, 0}, {1, 0, 1}}
Eigenvalues[A]
{1, 1, 1}
Eigenvectors[A]
{{0, -1, 1}, {0, 0, 0}, {0, 0, 0}}
A1 = IdentityMatrix[3] - A
{{0, -1, -1}, {1, 0, 0}, {-1, 0, 0}}
Eigenvalues[A1]
{0, 0, 0}
Eigenvectors[A1]
{{0, -1, 1}, {0, 0, 0}, {0, 0, 0}}
A2 = A1.A1
{{0, 0, 0}, {0, -1, -1}, {0, 1, 1}}
Eigenvalues[A2]
{0, 0, 0}
Eigenvectors[A2]
{{0, -1, 1}, {1, 0, 0}, {0, 0, 0}}
A3 = A2.A1
{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}

 

 

 

Return to Mathematica page

Return to the main page (APMA0330)
Return to the Part 1 Matrix Algebra
Return to the Part 2 Linear Systems of Equations
Return to the Part 3 Linear Systems of Ordinary Differential Equations
Return to the Part 4 Non-linear Systems of Ordinary Differential Equations
Return to the Part 5 Numerical Methods
Return to the Part 6 Fourier Series
Return to the Part 7 Partial Differential Equations