Diagonalizing Symmetric Matrices: Definition & Examples

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question 1 of 3

The matrix, A, is a _____.

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1. To diagonalize a symmetric matrix, A, we calculate Pt AP. The result is the matrix, D, where D is the diagonal matrix shown. The eigenvalues of A are _____.

2. If the eigenvector of a matrix is the vector, v1, shown below, then the length of v1 is _____.

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About This Quiz & Worksheet

Work through the quiz and worksheet to see what you know about diagonalizing symmetric matrices. The meaning of diagonalizing and the steps it involves are topics you need to know for the quiz.

Quiz & Worksheet Goals

These tools help you check your understanding of:

  • How to diagonalize a symmetric matrix
  • Diagonalizing a matrix
  • An eigenvector
  • Types of matrices

Skills Practiced

  • Reading comprehension - ensure that you draw the most important information from the lesson on diagonalizing symmetric matrices
  • Information recall - access the knowledge you have gained about the different types of matrices
  • Interpreting information - verify that you can read information about how to diagonalize a symmetric matrix and interpret it correctly

Additional Learning

You can review more about these concepts thanks to the lesson called Diagonalizing Symmetric Matrices: Definition & Examples. This lesson lets you:

  • Determine what a diagonal matrix is
  • Compare and contrast the different types of matrices
  • Identify the steps for diagonalizing a symmetric matrix
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