let n be Nat; :: thesis: for M being Matrix of n,REAL holds |:M:| is Nonnegative
let M be Matrix of n,REAL; :: thesis: |:M:| is Nonnegative
for i, j being Nat st [i,j] in Indices |:M:| holds
|:M:| * (i,j) >= 0

proof

let i, j be Nat; :: thesis: ( [i,j] in Indices |:M:| implies |:M:| * (i,j) >= 0 )
assume A1: [i,j] in Indices |:M:| ; :: thesis: |:M:| * (i,j) >= 0
Indices |:M:| = Indices M by Th5;
then |:M:| * (i,j) = |.(M * (i,j)).| by A1, Def7;
hence |:M:| * (i,j) >= 0 by COMPLEX1:46; :: thesis: verum

end;

hence |:M:| is Nonnegative ; :: thesis: verum