Properties of Determinants

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Taught by OCW
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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.
More info at: http://ocw.mit.edu/terms

Additional Resources:
Questions answered by this video:
  • What is a determinant?
  • What is an eigenvalue?
  • How do you find eigenvalues?
  • How do you find the determinant of a matrix?
  • When does a matrix have an inverse?
  • Staff Review

    • Currently 4.0/5 Stars.
    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.