Is it true that any unimodular matrix can be transformed into the identity matrix using only elementary row operations, i.e. multiplying a row by $-1$, exchanging two rows or summing one row to another? I cannot find a counterexample, so I suppose it is true, but I do not know how to prove it.
2026-03-25 11:17:50.1774437470
Unimodular matrices and row operations
204 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 ABELIAN-GROUPS
- How to construct a group whose "size" grows between polynomially and exponentially.
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- Invariant factor decomposition of quotient group of two subgroups of $\mathbb{Z}^n$.
- Computing Pontryagin Duals
- Determine the rank and the elementary divisors of each of the following groups.
- existence of subgroups of finite abelian groups
- Theorem of structure for abelian groups
- In the category of abelian groups the coequalizer $\text{Coker}(f, 0)$, $f: A \to B$ is simply $B/f(A)$.
- Commutator subgroup and simple groups
- Are there any interesting examples of functions on Abelian groups that are not homomorphisms?
Related Questions in BILINEAR-FORM
- Determination of symmetry, bilinearity and positive definitiness for a linear mapping
- Using complete the square to determine positive definite matrices
- Question involving orthogonal matrix and congruent matrices $P^{t}AP=I$
- Equivalent definitions of the signature of a symmetric matrix
- Complex integration and bilinear operators
- Hermitian form on a complex vector space: troubles!
- Can you show this is a bilinear form?
- Interpretation of transpose of a linear application from a matricial product point of view
- Prove that 1. $\kappa(x,y)$ is a symmetric bilinear form? 2. $\kappa([x,y],z)=\kappa(x,[y,z])$
- How does the non-degenerate symmetric bilinear form on $\mathfrak{h}$ induce a non-degenerate symmetric bilinear form on $\mathfrak{h}^*$?
Related Questions in UNIMODULAR-MATRICES
- Does this property imply total unimodularity?
- Is this block matrix totally unimodular?
- If matrix $A$ is totally unimodular, then matrix $\begin{bmatrix} A &\pm A\end{bmatrix}$ is also totally unimodular
- Find explicitely an element of SL$_2(\mathbb Z)$
- (reference-request) Theorem of Frobenius regarding transforming integer-valued matrix in diagonal matrix with divisibility conditions
- Proof $D_2^{-1}D_1$ is a unimodular matrix.
- Ring of invariants of unimodular matrices acting on real square matrices
- Reference for a result in Abelian Group Theory
- Totally Unimodular Matrices
- How can I compute a 3 by 3 unimodular matrix which produces an infinite number of Fermat near misses?
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?