Everything about Gell-Mann Matrices (Part 1): Unary Operations

Gell–Mann

λ

i

matrices

i

0

1

2

3

4

5

6

7

8

operations

λ

i

n

λ

i

θ

λ

i



eigensystem[

λ

i

]

n

2

3

4

λ

1

=

0	1	0
1	0	0
0	0	0

Gell–Mann

λ

-matrices are a complete set of Hermitian

3×3

noncommuting trace-orthogonal matrices,

Tr

λ

i

λ

j

=

δ

ij

,

i=1,…,8

. They are at the heart of Quantum Chromodynamics (QCD), an integral part of the Standard Model. They are also used in quantum information theory to represent qutrits. Gell–Mann matrices are to

SU(3)

what the Pauli matrices are to

SU(2)

.

This Demonstration shows operations involving a single

λ

-matrix.