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Coefficients

What are Eige...

Question

What are Eigenvalues of a Matrix?

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Solution

Eigenvalues are a special set of scalars associated with a linear system of equations.
Eigenvalues are also known as characteristic values.
The equation to find the eigenvalues of a given square matrix, $A$ is
$|A - λ I| = 0$
Where $I =$ Identity matrix and $λ =$ the eigenvalues of the matrix.

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Similar questions

Let A be a square matrix of order 2 or 3 and I will be the identity matrix of the same order. Then the matrix A -

λ

I is called the characteristic matrix of the matrix A, where

λ

is some complex number. The determinant of the characteristic matrix is called characteristic determinant of matrix A which will, of course, be a polynomial of degree 3 in

λ

. The equation det (A -

λ

=

0 is called the characteristic equation of the matrix A and its roots (the values of

λ

) are called characteristic roots or eigenvalues. It is also known that every square matrix has its characteristic equation.

The eigenvalues of the matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & 1 2 & 3 & 4 - 1 & - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦

λ

is a eigenvalue of A, then corresponding eigen value of

P^{- n} A P^{n}

(P is a square matrix with same order as A) is

Q. Which of the following matrices do not have eigenvalues as 1 and -1?

Q. If a eigenvalue of A is

λ

, then the corresponding eigen value of A

^{- 1}

P- symmetric matrix, Q- skew symmetric matrix, P and Q are square matrice of same order, then what type of a matrix is PQ-QP

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