New posts in orthogonality

Let $ V $ be an Euclidian space of dimension $n$ and let $v_1,...,v_m \in V$ s.t. $\langle v_i,v_j \rangle<0$ for all $i\neq j$. Show $m \leq n + 1 $

linear-algebra orthogonality

Finding $T^{\perp}$!

hilbert-spaces inner-products orthogonality

Showing that complex exponentials of the Fourier Series are an orthonormal basis

fourier-analysis fourier-series orthonormal orthogonality

Find all points on the surface where the normal line passes through the origin

vectors vector-analysis orthogonality

Finding vectors orthonormal to a given vector set and the Gram-Schmidt process

vectors inner-products orthogonality orthonormal

What is the difference between orthogonal and orthonormal in terms of vectors and vector space?

linear-algebra matrices orthogonality

Find the determinant of $A + I$, where $A$ is a real matrix such that $AA^{\top}=I$ and $\det A<0$.

linear-algebra matrices determinant orthogonality unitary-matrices

Why is the name "orthogonality"?

definition abelian-groups analytic-number-theory orthogonality dirichlet-character

Proving that matrices in $O(2)$ are of one of two forms

linear-algebra orthogonality orthonormal linear-groups

Orthogonal matrix norm

matrices orthogonality

Existence of orthogonal coordinates on a Riemannian manifold

riemannian-geometry coordinate-systems orthogonality

Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix

linear-algebra matrices orthogonality

Why is the matrix-defined Cross Product of two 3D vectors always orthogonal?

linear-algebra matrices inner-products orthogonality cross-product

Why can we reformulate $ \lvert \lvert Y-P_{[X]}Y\rvert \rvert ^{2}-\lvert \lvert Y-P_{[X_{0}]}Y\rvert \rvert ^{2}$ in the following way?

real-analysis linear-algebra matrices orthogonality projection

Is there an easy way to find the sign of the determinant of an orthogonal matrix?

linear-algebra matrices determinant computational-complexity orthogonality

What does it mean for two matrices to be orthogonal?

linear-algebra orthogonality

Do orthonormal changes of basis affect the inner product?

linear-algebra vector-spaces inner-products orthogonality orthonormal

Show $Q(x)\cdot Q(y)=x\cdot y\Rightarrow Q^TQ=I$

linear-algebra matrices orthogonality orthonormal

What can be said about a matrix which is both symmetric and orthogonal?

linear-algebra matrices inverse orthogonality

Basis to Hyperplane

linear-algebra orthogonality