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Matrix Product

Result

(28 | 33 | 29 28 | 31 | 31 28 | 33 | 29)

Dimensions

3 (rows) × 3 (columns)

Matrix plot

Matrix plot

Transpose

(28 | 28 | 28 33 | 31 | 33 29 | 31 | 29)

Trace

88

Determinant

0

Matrix rank

2

Nullity

1

Characteristic polynomial

-λ^3 + 88 λ^2 + 180 λ

Eigenvalues

λ_1 = 90

λ_2 = -2

λ_3 = 0

Eigenvectors

v_1 = (1, 1, 1)

v_2 = (33, -59, 33)

v_3 = (-31, 14, 14)

Diagonalization

(28 | 33 | 29 28 | 31 | 31 28 | 33 | 29) = S.J.S^(-1) where S = (33 | -31 | 1 -59 | 14 | 1 33 | 14 | 1) J = (-2 | 0 | 0 0 | 0 | 0 0 | 0 | 90) S^(-1) = (0 | -1/92 | 1/92 -1/45 | 0 | 1/45 14/45 | 33/92 | 1367/4140)

Condition number

∞

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