Register

Eigen values

• edited by
1,976 views
3 votes
3 votes

The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is 

A). $\pm i$

B), $(\pm i,\pm1)$

C). $\pm1$

D). $(0,\pm i)$

• edited by
User Avatar

1 Answer

2 votes
2 votes

Option (B) is correct.

To solve this question, we use two properties of eigen value of skew-symmetrical  matrix of order 'n'

1) If n=odd,eigen value is 0.

2) if  n = even,eigen values are pure imaginary.

Here n = 4(even),hence eigen values are +i,-i 

Now for orthogonal matrix,eigen value is either 1 or -1.

Hence option is (B).

±

• edited by
User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
1 answer
1
jaswanth431 asked Dec 12, 2021
277 views
Self doubt: what are eigen values of resultant matrix when add two matrices?
if eigen values of matrix A = a,b,c if eigen values of matrix B = x,y,z then is it holds every time that eigen value of A+B = a+x, b+y, c+z ? please give some reference to you answer, thankyou.
if eigen values of matrix A = a,b,cif eigen values of matrix B = x,y,zthen is it holds every time that eigen value of A+B = a+x, b+y, c+z ?please give some reference to y...
User Avatar
1 votes
1 votes
0 answers
2
Shamim Ahmed asked Jan 4, 2019
518 views
Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?
User Avatar
1 votes
1 votes
0 answers
4
Lakshman Bhaiya asked Oct 25, 2018
499 views
Eigen Values(Matrix is not idempotent)
Given that a matrix $A_{3\times3},$which is not idempotent matrix.And $A^{3}=A.$ Then find them, $1)$ Eigen Values $2)$ Trace of the matrix$=$Sum of Leading Diagonal Elements$=\sum a_{ij},$ where $i=j$ $3)Det(A)$
Given that a matrix $A_{3\times3},$which is not idempotent matrix.And $A^{3}=A.$Then find them,$1)$ Eigen Values$2)$ Trace of the matrix$=$Sum of Leading Diagonal Element...
User Avatar
Link Copied!