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.
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.
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This video begins an emphasis on square matrices by talking about determinants of matrices and their properties. A great intro video for understanding determinants, inverses, and eigenvalues of square matrices.