## Operator Precedence

You can build expressions that use any combination of arithmetic, relational, and logical operators. Precedence levels determine the order in which MATLAB® evaluates an expression. Within each precedence level, operators have equal precedence and are evaluated from left to right. The precedence rules for MATLAB operators are shown in this list, ordered from highest precedence level to lowest precedence level:

1. Parentheses `()`

2. Transpose `(.')`, power `(.^)`, complex conjugate transpose `(')`, matrix power `(^)`

3. Power with unary minus `(.^-)`, unary plus `(.^+)`, or logical negation `(.^~)` as well as matrix power with unary minus `(^-)`, unary plus `(^+)`, or logical negation `(^~)`.

### Note

Although most operators work from left to right, the operators `(^-)`, `(.^-)`, `(^+)`, `(.^+)`, `(^~)`, and `(.^~)` work from second from the right to left. It is recommended that you use parentheses to explicitly specify the intended precedence of statements containing these operator combinations.

4. Unary plus `(+)`, unary minus `(-)`, logical negation `(~)`

5. Multiplication `(.*)`, right division `(./)`, left division `(.\)`, matrix multiplication `(*)`, matrix right division `(/)`, matrix left division `(\)`

6. Addition `(+)`, subtraction `(-)`

7. Colon operator `(:)`

8. Less than `(<)`, less than or equal to `(<=)`, greater than `(>)`, greater than or equal to `(>=)`, equal to `(==)`, not equal to `(~=)`

9. Element-wise AND `(&)`

10. Element-wise OR `(|)`

11. Short-circuit AND `(&&)`

12. Short-circuit OR `(||)`

### Precedence of AND and OR Operators

MATLAB always gives the `&` operator precedence over the `|` operator. Although MATLAB typically evaluates expressions from left to right, the expression `a|b&c` is evaluated as `a|(b&c)`. It is a good idea to use parentheses to explicitly specify the intended precedence of statements containing combinations of `&` and `|`.

The same precedence rule holds true for the `&&` and `||` operators.

### Overriding Default Precedence

The default precedence can be overridden using parentheses, as shown in this example:

```A = [3 9 5]; B = [2 1 5]; C = A./B.^2 C = 0.7500 9.0000 0.2000 C = (A./B).^2 C = 2.2500 81.0000 1.0000 ```