haleywisman8841 haleywisman8841
  • 31-08-2019
  • Mathematics
contestada

Every orthogonal matrix is diagonalizable. O True O False

Respuesta :

wagonbelleville wagonbelleville
  • 04-09-2019

Answer:

FALSE

Step-by-step explanation:

the correct answer is FALSE

A matrix is said to be orthogonal when it is  multiplied by its own transpose then the matrix comes out to be Identity.

                                      [tex]A^T.A = I[/tex]

the basic condition for a matrix to be diagonalizable is that the matrix should be symmetric.

but an orthogonal matrix is not necessarily symmetric so, the statement is false.

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