A linear transfomation $h:\Bbb R^n\rightarrow\Bbb R^n$ is orthogonal iff carries a base $\mathcal V$ in an orthonormal base $\mathcal V'$.
113779
If $P$ is an orthogonal matrix its columns form an orthonormal set.
127882
Proofs involving orthonormal basis
59598
The vectors are orthonormal
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
37813
If $T\colon \mathbb R^n \to \mathbb R^n $ linear and $T^2 = kT$
18379
Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
111769
Why is inverse of orthogonal matrix is its transpose?
94378
Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
78648
Find an orthonormal basis for the subspace of $\mathbb R^4$
133711
Orthogonal basis for infinite-dimensional vector spaces
42606
Orthogonality for Binomial Coefficients
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
137180
Orthonormal basis with specific norm
75855
Show that $\det{(A + sxy^*)}$ is linear in $s$
151752
Example of a linear operator on some vector space with more than one right inverse.
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$