anonymous
  • anonymous
is the matrix diagonalisable?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
i understand how to figure out the diagonal of it but I'm not sure how to do it with a unknown number
anonymous
  • anonymous
@ganeshie8 could you please help? I'm really stuck on this

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dayakar
  • dayakar
In linear algebra, a diagonal matrix is a matrix (usually a square matrix) in which the entries outside the main diagonal (↘) are all zero. The diagonal entries themselves may or may not be zero. Thus, the matrix D = (di,j) with n columns and n rows is diagonal if: d_{i,j} = 0 \text{ if } i \ne j\ \forall i,j \in \{1, 2, \ldots, n\} For example, the following matrix is diagonal: \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & 0\\ 0 & 0 & -2\end{bmatrix} The term diagonal matrix may sometimes refer to a rectangular diagonal matrix, which is an m-by-n matrix with all the entries not of the form di,i being zero. For example: \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & 0\\ 0 & 0 & -3\\ 0 & 0 & 0\\ \end{bmatrix} or \begin{bmatrix} 1 & 0 & 0 & 0 & 0\\ 0 & 4 & 0& 0 & 0\\ 0 & 0 & -3& 0 & 0\end{bmatrix}
mathmate
  • mathmate
Hints: 1. A matrix is diagonalizable when it has distinct eigenvalues. 2. A triangular matrix has its eigenvalues on the main diagonal.
dayakar
  • dayakar
@mathmate what is eigenvalues mean
jango_IN_DTOWN
  • jango_IN_DTOWN
@dayakar a root of the characteristic equation
jango_IN_DTOWN
  • jango_IN_DTOWN
@swift_13 do you need the solution/?
thomas5267
  • thomas5267
We can say that if the unknown number is 0 for both cases then the matrices are diagonalisable since they are already diagonal already. For other cases I have to work it out.
thomas5267
  • thomas5267
Try writing down the matrices \(\lambda I-A\) and see what you get.
mathmate
  • mathmate
@dayakar Eigenvalues are the solution to the characteristic equation of the given matrix A, \(det (\lambda I-A)=0\) where det() means the "determinant of". For more information, read Paul's tutorial on the subject, or google other articles: http://tutorial.math.lamar.edu/Classes/DE/LA_Eigen.aspx

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