## Working with Linear Equality Constraints Using Portfolio Object

Linear equality constraints are optional linear constraints that impose systems of equalities on portfolio weights (see Linear Equality Constraints). Linear equality constraints have properties `AEquality`, for the equality constraint matrix, and `bEquality`, for the equality constraint vector.

### Setting Linear Equality Constraints Using the `Portfolio` Function

The properties for linear equality constraints are set using the `Portfolio` object. Suppose that you have a portfolio of five assets and want to ensure that the first three assets are 50% of your portfolio. To set this constraint:

```A = [ 1 1 1 0 0 ]; b = 0.5; p = Portfolio('AEquality', A, 'bEquality', b); disp(p.NumAssets) disp(p.AEquality) disp(p.bEquality)```
```5 1 1 1 0 0 0.5000```

### Setting Linear Equality Constraints Using the `setEquality` and `addEquality` Functions

You can also set the properties for linear equality constraints using `setEquality`. Suppose that you have a portfolio of five assets and want to ensure that the first three assets are 50% of your portfolio. Given a `Portfolio` object `p`, use `setEquality` to set the linear equality constraints:

```A = [ 1 1 1 0 0 ]; b = 0.5; p = Portfolio; p = setEquality(p, A, b); disp(p.NumAssets) disp(p.AEquality) disp(p.bEquality)```
```5 1 1 1 0 0 0.5000```

Suppose that you want to add another linear equality constraint to ensure that the last three assets also constitute 50% of your portfolio. You can set up an augmented system of linear equalities or use `addEquality` to build up linear equality constraints. For this example, create another system of equalities:

```p = Portfolio; A = [ 1 1 1 0 0 ]; % first equality constraint b = 0.5; p = setEquality(p, A, b); A = [ 0 0 1 1 1 ]; % second equality constraint b = 0.5; p = addEquality(p, A, b); disp(p.NumAssets) disp(p.AEquality) disp(p.bEquality)```
```5 1 1 1 0 0 0 0 1 1 1 0.5000 0.5000```

The `Portfolio` object, `setEquality`, and `addEquality` implement scalar expansion on the `bEquality` property based on the dimension of the matrix in the `AEquality` property.