It is known fact that if $U$ unitary matrix in $M_n(C)$ (i.e. $UU^*=U^*U=I$) then $U$ has square root $V$ which is also unitary matrix. But suppose that $U$ unitary matrix and $V\in M_n(C)$ such that $U=V^2$. Then is it true that the $V$ is also unitary matrix? thanks in advance.
2026-02-23 01:03:59.1771808639
Square root of unitary matrix
1.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related 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 MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in RADICALS
- Tan of difference of two angles given as sum of sines and cosines
- Symmetric polynomial written in elementary polynomials
- Interesting inequalities
- Prove that $\frac{1}{\sqrt{ab+a+2}}+ \frac{1}{\sqrt{bc+b+2}}+ \frac{1}{\sqrt{ac+c+2}} \leq \frac{3}{2}$
- Radical of Der(L) where L is a Lie Algebra
- Find local extrema $f(x_1,x_2, \ldots , x_n) = \sqrt{(x_1+x_2+\ldots x_n-a)(a-x_1)(a-x_2)\cdots (a-x_n)}$
- A non-geometrical approach to this surds question
- If $\sqrt{9−8\cos 40^{\circ}} = a +b\sec 40^{\circ}$, then what is $|a+b|$?
- Finding minimum value of $\sqrt{x^2+y^2}$
- Polynomial Equation Problem with Complex Roots
Related Questions in MATRIX-CALCULUS
- How to compute derivative with respect to a matrix?
- Definition of matrix valued smooth function
- Is it possible in this case to calculate the derivative with matrix notation?
- Monoid but not a group
- Can it be proved that non-symmetric matrix $A$ will always have real eigen values?.
- Gradient of transpose of a vector.
- Gradient of integral of vector norm
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- How to differentiate sum of matrix multiplication?
- Derivative of $\log(\det(X+X^T)/2 )$ with respect to $X$
Related Questions in UNITARY-MATRICES
- Operator norm and unitary matrix
- Unitary matrices are invertible.
- Square root of unitary matrix
- $AA^*A=A$ with eigenvalues $1$ and $0$, prove that $A$ is unitarily diagonalizable.
- Modifying unitary matrix eigenvalues by right multiplication by orthogonal matrix
- Parametrization of unitary matrices
- Is real power of unitary matrix unitary?
- How to calculate the unitaries satisfying $U_YXU_Y^\dagger=Y$ and $U_ZXU_Z^\dagger=Z$?
- A real symmetric cannot be similar to an antisymmetric matrix
- How are $SU(n)$, $SL(n)$ and $\mathfrak{sl}(n,\mathbb{C})$ related?
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?
No, e.g. with $$V=\pmatrix{1&1\\0&-1}$$ we have $V^2=I$ which is unitary but $V$ is not.