Can we prove that the eigenvalues of an $n\times n$ orthogonal matrix are $\pm 1$ by only using the definition of orthogonal matrix?
16562
what are the eigenvalues in orthgonal matrix, How to explain?
110271
Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
26801
Show that orthogonal matrices are diagonalizable
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
104293
How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
36064
How many $3 \times 3$ integer matrices are orthogonal?
149629
The Eigenvalues of a block matrix
1865
Sub-determinants of an orthogonal matrix
37794
Proving the two given vectors are orthogonal
123679
General Information about Eigenvalues for an 3x3 symmetric matrix
150376
Does Real Eigenvalues mean it is an hermitian Matrix
38436
If an orthogonal matrix has determinant -1 then it has -1 as an eigenvalue
52208
Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
16439
What are the eigenvalues of matrix that have all elements equal 1?
69542
Why do the $n \times n$ non-singular matrices form an "open" set?
52946
If $X$ is an orthogonal matrix, why does $X^TX = I$?