Applied Mathematics 1411A/B Lecture Notes - Lecture 18: Invertible Matrix, Diagonalizable Matrix, Diagonal Matrix
12 Mar 2015
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Recall: last day, we introduced the concept of eigenvalues and eigenvectors. Example: find the eigenvalues and bases for the eigenspaces of a where. Recall: on assignment #3, you had the opportunity to study markov chains. P is a matrix, called the transition matrix. Example (from our text): suppose that at some initial point in time 100,000 people live in a certain city and 25,000 live in its suburbs. The regional planning commission determines that each year 5% of the city population moves to the suburbs and 3% of the suburban population moves to the city. Definition: a differential equation is an equation that contains an unknown function and one or more of its derivatives. Find the eigenvalues and eigenvectors of a. 1 respectively, find matrix are 5, -1 and the corresponding eigenvectors are the solution of the system. Definition: a square matrix a is called diagonalizable if there is an invertible matrix p such that.
