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    Matrix Inverse

    Result

    1/12(-5 | 3 | 4 7 | 3 | -8 1 | -3 | 4)

    Expanded form

    (-5/12 | 1/4 | 1/3 7/12 | 1/4 | -2/3 1/12 | -1/4 | 1/3)

    Dimensions

    3 (rows) × 3 (columns)

    Matrix plot

    Matrix plot

    Transpose

    (-5/12 | 7/12 | 1/12 1/4 | 1/4 | -1/4 1/3 | -2/3 | 1/3)

    Trace

    1/6

    Determinant

    -1/12

    Characteristic polynomial

    -λ^3 + λ^2/6 + λ/2 - 1/12

    Eigenvalues

    λ_1 = -1/sqrt(2)

    λ_2 = 1/sqrt(2)

    λ_3 = 1/6

    Eigenvectors

    v_1 = (1/7 (-13 - 9 sqrt(2)), 1/7 (5 + 11 sqrt(2)), 1)

    v_2 = (1/7 (-13 + 9 sqrt(2)), 1/7 (5 - 11 sqrt(2)), 1)

    v_3 = (1, 1, 1)

    Diagonalization

    (-5/12 | 1/4 | 1/3 7/12 | 1/4 | -2/3 1/12 | -1/4 | 1/3) = P.D.P^(-1) where P≈(1 | -3.67542 | -0.0388683 1 | 2.93662 | -1.50805 1 | 1 | 1) D≈(0.166667 | 0 | 0 0 | -0.707107 | 0 0 | 0 | 0.707107) P^(-1)≈(0.323529 | 0.264706 | 0.411765 -0.182562 | 0.0756196 | 0.106942 -0.140967 | -0.340326 | 0.481293)

    Condition number

    9

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