Abstract: A method is given to prove that the n-dimensional normally distributed linear functions obey normal distribution. First,  the n-dimensional normally distributed linear function is expressed as the linear function of the n-dimensional standard normal distribution by the transitivity of linear transformation. Then, the linear function of n-dimensional normal distribution is proved to obey normal distribution by using the property that the linear functions of mutually independent normal distribution obey normal distribution.

Key words: n-dimensional normal distribution, n-dimensional standard normal distribution, linear transformation, linear function