In some questions of submanifold, I want to use determinant as a $C^{\infty}$Map, and show that, for example, $det^{-1}\{-1\}$ is a submanifold of $M_{2n}(\mathbb{R})$(this may be not true). However, I don't know what (J(det)) is(the Jacobian of determinant). Could you teach me??
2026-03-25 17:40:32.1774460432
What is the Jacobian of det???
70 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 MANIFOLDS
- a problem related with path lifting property
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- Using the calculus of one forms prove this identity
- "Defining a smooth structure on a topological manifold with boundary"
- On the differentiable manifold definition given by Serge Lang
- Equivalence of different "balls" in Riemannian manifold.
- Hyperboloid is a manifold
- Integration of one-form
- The graph of a smooth map is a manifold
Related Questions in JACOBIAN
- Finding $Ax=b$ iteratively using residuum vectors
- When a certain subfield of $\mathbb{C}(x,y^2)$ is Galois
- Two variables with joint density: Change of variable technique using Jacobian for $U=\min(X,Y)$ and $V=\max(X,Y)$
- Jacobian determinant of a diffeomorphism on the unit shpere must equal $1$ or $-1$
- Physicists construct their potentials starting from the Laplace equation, why they do not use another differential operator, like theta Θ?
- Solution verification: show that the following functions are not differentiable
- Finding Jacobian of implicit function.
- Jacobian chain rule for function composition with rotation matrix
- Is there a way to avoid chain rules in finding this derivative of an integral?
- Computing the derivative of a matrix-vector dot product
Related Questions in SUBMANIFOLD
- Subset of Open submanifold is a submanifold?
- Integrability of $\ker \alpha(X,.)$
- Restriction of a tensor to a submanifold
- Show that the sphere $S^{n}$ is a closed embedded submanifold of $\Bbb{R}^{n+1}$
- How do I find a Gauss map and what should it look like?
- Which of the following subsets are of classe $C^1$?
- The boundary of an open half-ball is contained in a union of two spheres ? (Lee's smooth manifold))
- Horizontal Submanifolds of Maximal Dimension
- Special orthogonal group is a submanifold
- Is there something like a partition of unity subordinate to something which is not a cover?
Related Questions in MAPPING-CLASS-GROUP
- generators for the mapping class group of a neighborhood of curves?
- Given the transformation $T:\Bbb R^5 \to\Bbb R^2$ where $T(x) = Ax$, how many rows and columns does matrix $A$ have?
- Fixed points of finite order mapping classes
- Any orientation-preserving automorphism of the annulus is isotopic to the identity
- Mapping Class Group acts properly discontinuous; Alexander method
- Mapping class group of $S^p \times S^q$
- Is there a solvable subgroup with finite index and finite type in the mapping class group of a surface?
- spin mapping class group of circles
- Commutativity in Mapping Class Groups
- Homeomorphisms of the 2-sphere $S^2$ fixing a set of points.
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?