Metamath Proof Explorer


Table of Contents - 11.5. The characteristic polynomial

According to Wikipedia ("Characteristic polynomial", 31-Jul-2019, https://en.wikipedia.org/wiki/Characteristic_polynomial): "In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix as coefficients.". Based on the definition of the characteristic polynomial of a square matrix (df-chpmat) the eigenvalues and corresponding eigenvectors can be defined.

  1. Definition and basic properties
    1. cchpmat
    2. df-chpmat
    3. chmatcl
    4. chmatval
    5. chpmatfval
    6. chpmatval
    7. chpmatply1
    8. chpmatval2
    9. chpmat0d
    10. chpmat1dlem
    11. chpmat1d
    12. chpdmatlem0
    13. chpdmatlem1
    14. chpdmatlem2
    15. chpdmatlem3
    16. chpdmat
    17. chpscmat
    18. chpscmat0
    19. chpscmatgsumbin
    20. chpscmatgsummon
    21. chp0mat
    22. chpidmat
    23. chmaidscmat
  2. The characteristic factor function G
    1. fvmptnn04if
    2. fvmptnn04ifa
    3. fvmptnn04ifb
    4. fvmptnn04ifc
    5. fvmptnn04ifd
    6. chfacfisf
    7. chfacfisfcpmat
    8. chfacffsupp
    9. chfacfscmulcl
    10. chfacfscmul0
    11. chfacfscmulfsupp
    12. chfacfscmulgsum
    13. chfacfpmmulcl
    14. chfacfpmmul0
    15. chfacfpmmulfsupp
    16. chfacfpmmulgsum
    17. chfacfpmmulgsum2
    18. cayhamlem1
  3. The Cayley-Hamilton theorem
    1. cpmadurid
    2. cpmidgsum
    3. cpmidgsumm2pm
    4. cpmidpmatlem1
    5. cpmidpmatlem2
    6. cpmidpmatlem3
    7. cpmidpmat
    8. cpmadugsumlemB
    9. cpmadugsumlemC
    10. cpmadugsumlemF
    11. cpmadugsumfi
    12. cpmadugsum
    13. cpmidgsum2
    14. cpmidg2sum
    15. cpmadumatpolylem1
    16. cpmadumatpolylem2
    17. cpmadumatpoly
    18. cayhamlem2
    19. chcoeffeqlem
    20. chcoeffeq
    21. cayhamlem3
    22. cayhamlem4
    23. cayleyhamilton0
    24. cayleyhamilton
    25. cayleyhamiltonALT
    26. cayleyhamilton1