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How To Add Matrices

Result

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

Dimensions

3 (rows) × 3 (columns)

Matrix plot

Matrix plot

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

M = S.J.S^(-1) where M = (5 | 7 | 9 9 | 7 | 5 5 | 8 | 8) S = (1 | 1/642 (195 + 163 i sqrt(15)) | 1/642 (195 - 163 i sqrt(15)) 1 | -1/321 i (71 sqrt(15) + -402 i) | 1/321 i (71 sqrt(15) + 402 i) 1 | 1 | 1) J = (21 | 0 | 0 0 | -1/2 i (sqrt(15) + -i) | 0 0 | 0 | 1/2 i (sqrt(15) + i)) S^(-1) = (71/233 | 163/466 | 161/466 (-355 - 241 i sqrt(15))/2330 | (i (149 sqrt(15) + 815 i))/4660 | (1525 + 333 i sqrt(15))/4660 (-355 + 241 i sqrt(15))/2330 | (-815 - 149 i sqrt(15))/4660 | (1525 - 333 i sqrt(15))/4660)

Condition number

27

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