Are roots of $\det(A-tB)$ with symmetric matrices real?
33891
If $\mathbf A$ and $\mathbf B$ are Hermitian, when does $\det(\mathbf A-\lambda\mathbf B)=0$ have only real roots?
110200
Determinant of a Special Symmetric Matrix
128723
The determinant of adjugate matrix
15202
the root of $N$th transpose matrix
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
18012
Eigenvectors of real symmetric matrices are orthogonal
78298
On the nilpotence of the matrix $AB-BA$
45527
Do real matrices always have real eigenvalues?
153816
Real Roots and Differentiation
143793
If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
40154
Finding the dimension of real symmetric matrices with trace zero
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
132213
Is every real monic polynomial the characteristic polynomial of a real matrix?
99600
Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
106011
Proving it has all real roots
27778
Eigenvalues of a real skew symmetric matrix
39256
Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$