Two events are mutually exclusive, if they are independent.

Let be a smooth surface in and its boundary is the positively oriented curve . If is a continuously differentiable vector field, then

For any vector fields the line integral is path independent, that is if and have common starting and ending points, then

The function has a local minimum at if for any one has for .

If the directional derivative of the function in the direction at is positive, then moving from in the direction the function is decreasing.

In a vector sequence is divergent if and only if all its coordinate sequences are divergent.

In an orthogonal system the vectors are orthogonal to each other.

For any three vectors , , one has .

If , then is a linear map.

The cumulative density function of the normal distribution is