Perpendicular vectors of equal length and orthogonal matrices
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
60571
Interweaving vectors
153028
Showing that the product of vector magnitudes is larger than their dot product
134652
Prove that the perpendicular bisectors of the sides of a triangle meet at a point
145885
Linear transformation preserving orthogonality
134131
Squared norm of matrix equal to squared norm of its transpose
2743
Dot Product and Cross Product: Solving a set of Simultaneous Vector Equations
112362
fixed point problem for orthogonal transformation
142097
Finding the dimension of the orthogonal complement
35247
The characteristic and minimal polynomial of a companion matrix
26801
Show that orthogonal matrices are diagonalizable
48579
How to find the orthogonal complement of a subspace?
52564
$m\times n$ matrix with an even number of 1s in each row and column
12955
Classification of $n\times n$ real matrices up to congruence
32064
Zero-dimensional matrices
63260
Matrices whose Linear Combinations are All Singular
108567
Nielsen & Chuang Exercise 2.2 - “Matrix representations: example”