I usually use thisCase for private methods and ThatCase for public methods.
private Vector add(Vector vector) {
for (int index = 0; index < Length; index++) {
this[index] += vector[index];
}
return this;
}
public Vector Add(Vector vector) {
for (int index = 0; index < Length; index++) {
this[index] += vector[index];
}
return this;
}