All Linear Algebra Resources
Example Questions
Example Question #11 : Eigenvalues And Eigenvectors Of Symmetric Matrices
Example Question #471 : Operations And Properties
Example Question #552 : Linear Algebra
Example Question #481 : Operations And Properties
Example Question #15 : Eigenvalues And Eigenvectors Of Symmetric Matrices
,
where is a real number.
For to have two real eigenvalues, what must be true for
?
or
or
can be any real number.
can be any real number.
Any real value of makes
a symmetric matrix with real entries. It holds that any eigenvalues of
must be real regardless of the value of
.
Example Question #561 : Linear Algebra
Give the set of eigenvalues of in terms of
, if applicable.
The eigenvalues are and
.
The only eigenvalue is 0.
The eigenvalues are 0 and .
The only eigenvalue is .
The eigenvalues are 0 and .
The eigenvalues are 0 and .
An eigenvalue of is a zero of the characteristic equation formed from the determinant of
, so find this determinant as follows:
Subtracting elementwise:
Set the determinant to 0 and solve for :
The determinant can be found by taking the upper-left-to-lower-right product and subtracting the upper-right-to-lower-left product:
,
so the eigenvalues of this matrix are 0 and .
Certified Tutor
All Linear Algebra Resources
