If $X$ is a skew-symmetric matrix, its exponential $e^X$ is orthogonal. Does the converse implication hold?
2025-01-13 07:52:33.1736754753
Conditions for $e^X$ to be an orthogonal matrix
108 Views Asked by Matt Dickau https://math.techqa.club/user/matt-dickau/detail AtRelated Questions in MATRICES
- Show CA=CB iff A=B
- What is the correct chain rule for composite matrix functions?
- Is the row space of a matrix (order n by m, m < n) of full column rank equal to $\mathbb{R}^m$?
- How to show that if two matrices have the same eigenvectors, then they commute?
- Linear Algebra: Let $w=[1,2,3]_{L_1}$. Find the coordinates of w with respect to $L$ directly and by using $P^{-1}$
- How to prove the cyclic property of the trace?
- Matrix expression manipulation
- Matrix subring isomorphic to $\mathbb{C}$
- Is the ellipsoid $x'Qx < \alpha$ equivalent to $\alpha Q^{-1} - x x' \succ 0$?
- Show that matrix $M$ is not orthogonal if it contains column of all ones.
Related Questions in ORTHOGONAL-MATRICES
- Orthogonality of stochastic matrix
- How to show that the isotropic tensor of order $n$ is a multiple of the Kronecker delta?
- The set of traces of orthogonal matrices is compact
- Find a real orthogonal matrix of order $3$ , other than +- I_3 ,having all integer elements.
- Parametrization of $3 \times 3$ real orthogonal matrices
- Show that $O(n)$, the set of orthogonal $n \times n$ matrices, is not connected
- Given matrices $A,B$, minimize $\|UAV^T - B\|_F$ over orthogonal matrices $U, V$
- Is an orthogonal matrix necessarily a permutation matrix?
- Orthogonal matrix $Q$ such that $\forall x\leq 0$, $Qx\geq 0$
- Show that $x$ and $Q x$ are equidistant
Related Questions in MATRIX-EXPONENTIAL
- General formula for the exponential of a block matrix
- Approximation for integral of Matrix Exponential
- Matrix exponential of non diagonalizable matrix?
- Norm-bound for triangular Hurwitz matrix exponential
- Scalar by matrix derivative $\frac{d {\rm tr} (e^{\bf X} {\bf A})}{d {\bf X}}$
- Let $A\in M_n(\mathbb{R})$. Show that $\lim_{n \to \infty} \bigg( I + \frac{A}{n}\bigg)^n = e^A$
- Is there a diagonalizable matrix $A \neq B$ such that $e^A = e^B$?
- For which classes of matrix can the matrix exponential be easily computed?
- Trace of Matrix Exponential closed form expression
- Derivative of matrix exponential at $0$
Related Questions in SKEW-SYMMETRIC-MATRICES
- Prove that the determinant of skew-symmetric matrices of odd order is zero
- When can two matrices be simultaneously skewsymmetrized?
- On the rank of antisymmetric matrices
- Sum of squares of skew-symmetric matrices which is not a square itself
- Find the rank of the matrix $M$
- The squares of skew-symmetric matrices span all symmetric matrices
- Does every negative semidefinite matrix lie in the convex cone generated by the squares of skew-symmetric matrices?
- The boundary of the convex hull of squares of skew-symmetric matrices
- Proof the following properties of antisymmetric matrices:
- Conditions for $e^X$ to be an orthogonal matrix
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity