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    Adding Matrices

    Result

    (5 | 7 | 9 9 | 7 | 5 5 | 8 | 8)

    Dimensions

    3 (rows) × 3 (columns)

    Matrix plot

    Matrix plot

    Transpose

    (5 | 9 | 5 7 | 7 | 8 9 | 5 | 8)

    Trace

    20

    Determinant

    84

    Inverse

    1/84(16 | 16 | -28 -47 | -5 | 56 37 | -5 | -28)

    Characteristic polynomial

    -λ^3 + 20 λ^2 + 17 λ + 84

    Eigenvalues

    λ_1 = 21

    λ_2 = 1/2 (-1 + i sqrt(15))

    λ_3 = 1/2 (-1 - i sqrt(15))

    Eigenvectors

    v_1 = (1, 1, 1)

    v_2 = (1/642 (195 - 163 i sqrt(15)), 1/321 (-402 + 71 i sqrt(15)), 1)

    v_3 = (1/642 (195 + 163 i sqrt(15)), 1/321 (-402 - 71 i sqrt(15)), 1)

    Diagonalization

    (5 | 7 | 9 9 | 7 | 5 5 | 8 | 8) = P.D.P^(-1) where P≈(1 | 0.303738 + 0.983328 i | 0.303738 - 0.983328 i 1 | -1.25234 - 0.856641 i | -1.25234 + 0.856641 i 1 | 1 | 1) D≈(21 | 0 | 0 0 | -0.5 - 1.93649 i | 0 0 | 0 | -0.5 + 1.93649 i) P^(-1)≈(0.304721 | 0.349785 | 0.345494 -0.152361 - 0.400596 i | -0.174893 + 0.123836 i | 0.327253 + 0.27676 i -0.152361 + 0.400596 i | -0.174893 - 0.123836 i | 0.327253 - 0.27676 i)

    Condition number

    27

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