Matrix

  1. Create:A
    • y=100020003×6 >>>y=60001200018

    • y=matrix([[1,0,0],[0,2,0],[0,0,3]])*6 >>>y=60001200018

  2. Determinant:|A|
    • m=123456789 det(m) >>>0

  3. Rank:R(A)
    • A=1235 R(A) >>>2

    • rank(A) >>>2

  4. Transposition:AT
    • m=1234567189 mT >>>1472518369

    • transpose(m) >>>1472518369

  5. Adjugate:A*
    • m=1234567189 m* >>>-6336-36-12637-4-3

    • adjugate(m) >>>-6336-36-12637-4-3

  6. Inverse: A -1
    • m=1234567189 m-1 >>>-1.050.6-0.050.1-0.20.10.616666666666667-0.0666666666666667-0.05

    • inv(m) >>>-1.050.6-0.050.1-0.20.10.616666666666667-0.0666666666666667-0.05

  7. Eigenvalues:EigVal
    • A= 3-24-2 53-3-2 5-22-2 5-2-33 EigVal(A) >>>{-2:1,3:1,5:2}

    Matrix A has eigenvalues -2, 3, and 5, and that the eigenvalues -2 and 3 have algebraic multiplicity 1 and that the eigenvalue 5 has algebraic multiplicity 2.

  8. Eigenvectors:EigVec
    • A= 3-24-2 53-3-2 5-22-2 5-2-33 EigVec(A) >>> (-2,1, 0 1 1 1 ), (3,1, 1 1 1 1 ), (5,2, 1 1 1 0 , 0 -1 0 1 )

  9. Dot product:a·b
    • v1=123 v2=456 dot(v1,v2) >>>32

  10. Cross product:a×b
    • v1=123 v2=456 cross(v1,v2) >>>-36-3

  11. LUdecomposition:LU
    • A=431.51 L,U=LU(A) >>>L=100.3751 >>>U=430-0.125

  12. QRdecomposition:QR
    • A=111113234 Q,R=QR(A) >>>Q=0.408248290463863-0.577350269189626-0.7071067811865480.408248290463863-0.5773502691896260.7071067811865480.8164965809277260.5773502691896260 >>>R=2.449489742783183.26598632371094.8989794855663600.5773502691896260001.4142135623731

  13. Diagonalize:Diag
    • A=1200302-42 P,D=Diag(A) >>>P=-10-100-1212 >>>D=100020003