public void SymmetricMatrixNorms()
{
SymmetricMatrix Z = new SymmetricMatrix(3);
Assert.IsTrue(Z.OneNorm() == 0.0);
Assert.IsTrue(Z.InfinityNorm() == 0.0);
Assert.IsTrue(Z.FrobeniusNorm() == 0.0);
SymmetricMatrix A = CreateSymmetricRandomMatrix(4, 1);
Assert.IsTrue(A.OneNorm() > 0.0);
Assert.IsTrue(A.InfinityNorm() > 0.0);
Assert.IsTrue(A.FrobeniusNorm() > 0.0);
SymmetricMatrix B = CreateSymmetricRandomMatrix(4, 2);
Assert.IsTrue(B.OneNorm() > 0.0);
Assert.IsTrue(B.InfinityNorm() > 0.0);
Assert.IsTrue(B.FrobeniusNorm() > 0.0);
SymmetricMatrix S = A + B;
Assert.IsTrue(S.OneNorm() <= A.OneNorm() + B.OneNorm());
Assert.IsTrue(S.InfinityNorm() <= A.InfinityNorm() + B.InfinityNorm());
Assert.IsTrue(S.FrobeniusNorm() <= A.FrobeniusNorm() + B.FrobeniusNorm());
SquareMatrix P = A * B;
Assert.IsTrue(P.FrobeniusNorm() <= A.FrobeniusNorm() * B.FrobeniusNorm());
// Frobenium norm is sub-multiplicative
}
