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Matrix Multiplication
Result
(28 | 33 | 29 28 | 31 | 31 28 | 33 | 29)
Dimensions
3 (rows) × 3 (columns)
Matrix plot
Transpose
(28 | 28 | 28 33 | 31 | 33 29 | 31 | 29)
Cofactors
(-124 | 56 | 56 0 | 0 | 0 124 | -56 | -56)
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) = P.D.P^(-1) where P = (33 | -31 | 1 -59 | 14 | 1 33 | 14 | 1) D = 2(-1 | 0 | 0 0 | 0 | 0 0 | 0 | 45) P^(-1) = 1/4140(0 | -45 | 45 -92 | 0 | 92 1288 | 1485 | 1367)
Condition number
∞