Linear Algebra and the C Language/a0lz

An eigenvector is a vector that has its direction unchanged (or reversed) by a given linear transformation ... Wikipedia: Eigenvalues and eigenvectors

To study this work you must have seen those on Gauss-Jordan Partial Pivoting and Free Variables

Two identical eigenvalues :

• Verify with Octave:
• c01a.c

• Calculate the two eigenvectors of the two identical eigenvalues:
• c01b.c

• Calculate the last eigenvector:
• c01c.c

• Check the calculation:
• c01d.c

Three identical eigenvalues :

• Verify with Octave:
• c02a.c

• Calculate the three eigenvectors of the three identical eigenvalues:
• c02b.c

• Calculate the last eigenvector:
• c02c.c

• Check the calculation:
• c02d.c

Twice two identical eigenvalues :

• Verify with Octave:
• c03a.c

• Calculate the two first eigenvectors of the two first identical eigenvalues:
• c03b.c

• Calculate the two last eigenvectors of the two last identical eigenvalues:
• c03c.c

• Check the calculation:
• c03d.c

Three identical zero eigenvalues :

• It’s possible that the process for calculating multiple eigenvalues will diverge and produce incorrect results.We can obtain these values through Octave, and then calculate the eigenvectors in the same way as previously.
• Verify with Octave:
• c04a.c

• Calculate the three eigenvectors of the three identical zero eigenvalues:
• c04b.c

• Calculate the last eigenvector:
• c04c.c

• Check the calculation:
• c04d.c