I need to give an example of a matrix $Q$ that has orthonormal columns but $QQ^T\ne I$. So my thinking is the following:
$ Q = \begin{bmatrix} 1&0 \\0 & 1 \\0 &0 \end{bmatrix} $ I know that these columns are orthonormal but what does $I$ refer to?
2026-03-28 01:35:13.1774661713
give an example of a matrix $Q$ that has orthonormal columns but $QQ^T\ne I$
210 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in ORTHONORMAL
- Orthonormal basis for $L^2(\mathbb{R}^n,\mathbb{F})$
- What is $\| f \|$ where $f(x)=\sum\limits_{n=1}^\infty \frac{1}{3^n} \langle x,e_n\rangle$
- Forming an orthonormal basis with these independent vectors
- Orthogonal Function Dirac Delta Series
- Sum of two rank $1$ matrices with some property gives rank $2$ matrix
- Zero element in an Hilbert space is orthogonal?
- Prove that $\lVert X\rVert^2 =\sum_{i,j=1}^\infty\lvert\langle u_i,Xu_j\rangle\rvert^2$.
- Is there any connection between the fact that a set of vectors are mutually orthogonal and the same set of vectors are linearly independent
- Compute the norm of a linear operator using a normal basis in an infinite Hilbert space
- If $M$ is the span of a finite orthonormal set in a Hilbert space then $M$ is closed
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?