-norm: If we denote as the total number of rich people in our city, than a compact way to calculate would be to use the -norm: Similarly, if we denote as the total number of poor people in our city, then: When we divide a vector by its norm, we get what is called the normalized vector or Unit vector : Let us normalize the rich vector and the poor vector : We finally return to the formula for the Index of Dissimilarity (); it is simply equal to one-half the -norm of the difference between the vectors and : Numerical example Consider a city consisting of four blocks of 2 people each. One block consists of 2 rich people. One block consists of 2 poor people. Two blocks consist of 1 rich and 1 poor person. What is the index of dissimilarity for this city? Firstly, let's find the rich vector and poor vector : Next, let's calculate the total number of rich people and poor people in our city: Next, let's normalize the rich and poor vectors: We can now calculate the difference : Finally, let's find the index of dissimilarity (): Equivalence between formulae We can prove that the Linear Algebraic formula for is identical to the basic formula for . Let's start with the Linear Algebraic formula: Let's replace the normalized vectors and with: Finally, from the definition of the -norm, we know that we can replace it with the summation: Thus we prove that the linear algebra formula for the index of dissimilarity is equivalent to the basic formula for it: Zero segregation When the Index of Dissimilarity is zero, this means that the community we are studying has zero segregation. For example, if we are studying the segregation of rich and poor people in a city, then if , it means that: There are no blocks in the city which are "rich blocks", and there are no blocks in the city which are "poor blocks" There is a homogeneous distribution of rich and poor people throughout the city If we set in the linear algebraic formula, we get the necessary condition for having zero segregation: For example, suppose you have a city with 2 blocks. Each block has 4 rich people and 100 poor people: Then, the total number of rich people is , and the total number of poor people is . Thus: