Exercise of symmetric matrices
94383
Prove that $A^TD-C^TB=I$
70021
Verify if symmetric matrices form a subspace
17584
Integer matrices with integer inverses
48113
Find a basis for the vector space of symmetric matrices with an order of $n \times n$
31029
Characteristic polynomial of a matrix of $1$'s
54628
Properties of non-zero symmetric bilinear form
26801
Show that orthogonal matrices are diagonalizable
124095
$A$ is a real orthogonal matrix, prove that $ (I+A)^{-1}(I-A)$ is skew-symmetric
30665
Elegant proofs that similar matrices have the same characteristic polynomial?
57027
Determinant of this skew symmetric matrix
19132
Similar matrices have the same eigenvalues with the same geometric multiplicity
30877
How to show that the set of orthogonal n x n matrices forms a group under multiplication
52564
$m\times n$ matrix with an even number of 1s in each row and column
58595
Existence of a G-invariant matrix
20920
Determinant of a block skew-symmetric matrix
8627
Number of equivalence classes of $w \times h$ matrices under switching rows and columns
8356
Any $n \times n$ matrix $A$ can be written as $A = B + C$ with $B$ is symmetric and $C$ skew-symmetric.