I am attempting to transform the components of a mesh directly using a 4x4 matrix. This is working for the vertex positions, but it is not working for the normals (and probably not the tangents either).

Here is what I have:

// Transform vertex positions - Works like a charm!
vertices = mesh.vertices;
for (int i = 0; i < vertices.Length; ++i)
    vertices[i] = transform.MultiplyPoint(vertices[i]);

// Does not work, lighting is messed up on mesh
normals = mesh.normals;
for (int i = 0; i < normals.Length; ++i)
    normals[i] = transform.MultiplyVector(normals[i]);

Note: The input matrix converts from local to world space and is needed to combine multiple meshes together.