On the basis of the paper [1]

this paper defined the level-q (ki)-circulant ma- trices and its the subblocks of notatian

and obtained: 1°. Let A =k1 - circ (A0

A1

…

An1-1 be a level-q(K1

K2

…

kq)-circu- lant matrix of type (n1

n2

…

nq)

where q is a natural number

and its the subblocks of notatian are A_(i1 i2 … iq-1)=kq-circ(a_(i1 i2 … iq-10)

a_(i1 i2 … iq-11)

…

a_(i1 i2 … iq-1 nq-1))

i1 =0

1

…

n1-1

t=1

2

…

q-1

then the eigenvalues of A where ωi is a primitive ni th root of unity

μi is a ni th root of ki

i =1

2

…

q. 2°Let a matrix A as well as 1°

and |ki| =1

i=1

2

…

q

Z={a=(j1

j2

… …

jq) |λj1 J2 … jq =0

1≤ji≤ni

i = 1

…

q}

then a Moore-Penrose inverse of A A+ = (A + K )-1-K

where K = ∑Ka

and Ka = K_(j1 (?) Kj2_(?)…(?)Kjq

and