- #1
rugerts
- 153
- 11
- Homework Statement
- Find general solution of DE
- Relevant Equations
- Eigenvector and eigenvalue eqns
Thanks for your time
You are right and i was wrong. We have only a one dimensional eigenspace, spanned by a single vector.pasmith said:If the eigenspace is the entire space, there's no reason not to use the standard basis.
A free variable in the context of generalized eigenvectors refers to a variable that can take on any value, without affecting the solution of a system of linear equations. It is often used when finding generalized eigenvectors to simplify the process and make the calculations easier.
The free variable is typically chosen based on the structure of the matrix and the specific eigenvalue being considered. It is usually selected to make the calculations as simple as possible, and can vary depending on the specific problem being solved.
Choosing a free variable allows for a simpler and more efficient method of finding generalized eigenvectors. It also helps to reduce the number of calculations needed and can provide a more elegant solution to the problem.
There are no strict rules for choosing a free variable, as it ultimately depends on the specific problem being solved. However, it is important to choose a variable that simplifies the calculations and does not affect the overall solution.
No, the choice of free variable does not affect the final solution for generalized eigenvectors. As long as the free variable is chosen correctly and does not affect the calculations, the end result will be the same regardless of which variable is chosen.