# Properties of Determinants

Taught by OCW
• Currently 4.0/5 Stars.
5959 views | 1 rating
Part of video series
Lesson Summary:

In this Properties of Determinants lesson, the instructor emphasizes the importance of determinants in finding eigenvalues and goes over three key properties of determinants: the determinant of identity is one, exchanging two rows reverses the sign of the determinant, and the determinant is a linear function of each row. These properties lead to a formula for the determinant of a square matrix and also provide tests for invertibility and singularities. The lesson concludes with the determinant of an upper triangular matrix being the product of its diagonal entries.

Lesson Description:

Properties of Determinants -- Lecture 18. Properties of determinants and finding determinants and eigenvalues of square matrices.

Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 22, 2008). License: Creative Commons BY-NC-SA.

• 