Join experts in discussing linear and abstract algebra topics. This includes vector spaces and linear transformations. Also groups and other algebraic structures along with Number Theory.
Threads
Finding a Basis for a Linear Subspace Orthogonal to a Given Point P in R^3
- JWS1
- · Replies 2 ·
Undergrad Determinant and linear-algebraic aspects of Sudoku puzzles
- WWGD
- · Replies 7 ·
Undergrad How to Show U|v⟩ = e^(ia)|v⟩ for Unitary Operators?
- Peter_Newman
- · Replies 12 ·
Undergrad Proving ##\partial^{i} = g^{ik} \partial_{k}##
- SplinterCell
- · Replies 8 ·
Undergrad Why are determinants in 2x2 matrices and 3x3 matrices computed the way they are?
- Ale_Rodo
- · Replies 13 ·
Undergrad Why is gcd(x,n) either n or p when p divides x and n=pq?
- Peter_Newman
- · Replies 8 ·
Undergrad I think I've hit upon a very easy proof of impossibility of quintic
- swampwiz
- · Replies 2 ·
Matrix Transforms: nxm, n->m, m->n, n+m->n/m
- Imiebee
- · Replies 3 ·
Undergrad The tensor product of tensors confusion
- GR191511
- · Replies 32 ·
High School Is it invalid to redefine the sgn function in this way in a proof?
- Eclair_de_XII
- · Replies 15 ·
High School Solutions for universal linear recursions
- coolul007
- · Replies 7 ·
Graduate Center of a linear algebraic group
- fresh_42
- · Replies 9 ·
High School Proving the uniqueness of eigenspaces
- Eclair_de_XII
- · Replies 6 ·
QR decomposition with permutation matrix
- mathmari
- · Replies 6 ·
Approximation of eigenvalue with inverse iteration method
- mathmari
- · Replies 2 ·
Scalar Triple Product and Coplanarity
- brinlin
- · Replies 3 ·
Householder method : Which α do we take?
- mathmari
- · Replies 4 ·
Undergrad Central Extension and Cohomology Groups
- giulio_hep
- · Replies 7 ·
Undergrad Prove that the limit of this matrix expression is 0
- lriuui0x0
- · Replies 5 ·
High School Any square matrix can be expressed as the sum of anti/symmetric matrices
- Eclair_de_XII
- · Replies 7 ·
High School Geometrical meaning of magnitude of vector product
- songoku
- · Replies 9 ·
Find Vector of Given Length in Particular Direction
- brinlin
- · Replies 1 ·
What is the Angle Between Vectors Using the Dot Product Formula?
- brinlin
- · Replies 4 ·
Find Vector Perpendicular to Plane
- brinlin
- · Replies 3 ·
Graduate Link between 24 dimension kissing number and Monster group
- Labyrinth
- · Replies 7 ·
Undergrad How to Find the Generalized Eigenvector in a Matrix ODE?
- Alwar
- · Replies 10 ·
Examples of vector spaces over different fields
- nweissma
- · Replies 1 ·
Proving Non-Degeneracy of Euclidean Inner Products
- steenis
- · Replies 8 ·
Graduate A problem in multilinear algebra
- steenis
- · Replies 2 ·
High School Regarding Contravarient Vector Transformations
- AdvaitDhingra
- · Replies 25 ·
Undergrad Proving (x,x) = 0 implies x = 0 in real vector space V
- steenis
- · Replies 21 ·
Velocity and acceleration vectors and their magnitudes
- WMDhamnekar
- · Replies 8 ·
Understanding Velocity and Acceleration of a Moving Particle
- WMDhamnekar
- · Replies 2 ·
Undergrad Shouldn't this definition of a metric include a square root?
- nomadreid
- · Replies 8 ·
How is Radius of Curvature Computed for a Given Curve?
- WMDhamnekar
- · Replies 2 ·
Prove R is a Sub-ring of $\mathbb{Q}$ - Prime $p \in \mathbb{Z}$
- fabiancillo
- · Replies 11 ·
Undergrad Proving that ##V = U_1 \oplus U_2 \oplus \ldots \oplus U_k##
- JD_PM
- · Replies 6 ·
Undergrad Why pairwise intersections don't define direct sums of three subspaces
- JD_PM
- · Replies 7 ·
Diagonalizable transformation - Existence of basis
- mathmari
- · Replies 52 ·
Undergrad How to show span(U₁∪...∪Uₖ₋₁) + Uₖ = span(U₁∪...∪Uₖ)
- JD_PM
- · Replies 10 ·
Is the Matrix A Diagonalizable with Real Eigenvalues?
- mathmari
- · Replies 10 ·
High School Commutators of functions of operators
- LagrangeEuler
- · Replies 2 ·
Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
- karush
- · Replies 2 ·
Undergrad Meaning of terms in a direct sum decomposition of an algebra
- Rabindranath
- · Replies 8 ·
Graduate Lie Bracket * Matrix * vector (Need proof)
- Trying2Learn
- · Replies 9 ·
What is the velocity vector after a pinball bounces off a baffle?
- WMDhamnekar
- · Replies 4 ·
Undergrad How is unit norm axis rotation represented and derived in R3?
- LCSphysicist
- · Replies 4 ·
Undergrad Dimension of a Linear Transformation Matrix
- patric44
- · Replies 4 ·
Is the Calculated Osculating Plane and Binormal Correct for $\theta=0$?
- WMDhamnekar
- · Replies 1 ·
Prove $10^{\dfrac{5^n -1}{4}} \Huge\vert (5^n)!$ for $Z^+$
- karush
- · Replies 6 ·
Undergrad Canonical Form for quadratic equations *with* linear terms
- arestes
- · Replies 4 ·
Undergrad Two ways to define operations in a vector space
- Santiago24
- · Replies 7 ·
Undergrad Un-skewing a skew symmetric matrix (for want of a better phrase)
- Trying2Learn
- · Replies 1 ·
High School Magnitudes of the sum of two vectors
- keroberous
- · Replies 6 ·
Find the elementary divisors and invariant factors
- fabiancillo
- · Replies 2 ·
Undergrad How can the Lp Norm be used to prove inequalities?
- ashah99
- · Replies 9 ·
Undergrad Does the cross product determinant formula work in spherical and cylindrical coordinates?
- dyn
- · Replies 5 ·
The product γ is a rotation or a translation
- mathmari
- · Replies 11 ·
What are the properties of affine bases in $\mathbb{R}^n$?
- mathmari
- · Replies 15 ·
Checking if $\beta \in \text{Isom}(\mathbb{R}^2)$
- mathmari
- · Replies 15 ·
Graduate Multinomial functions of matrices
- Stephen Tashi
- · Replies 3 ·
Set of 2-dimensional orthogonal matrices equal to an union of sets
- mathmari
- · Replies 9 ·
Graduate Trace of the inverse of matrix products
- nikozm
- · Replies 2 ·
Undergrad What conditions are needed to raise a linear operator to some power?
- fxdung
- · Replies 4 ·
Undergrad Commutative algebra and differential geometry
- dx
- · Replies 3 ·
High School Explicit expression for ideal membership
- aheight
- · Replies 3 ·
Hectares and kilometres - how many days to cut 295 hectares
- Kzerr
- · Replies 3 ·
Undergrad One-Time Pad and Frequency Analysis
- Haku
- · Replies 16 ·
3.2.5.3 General Solution if system
- karush
- · Replies 14 ·
Solving 2nd-Order IVP as System of Equations
- karush
- · Replies 2 ·
Graduate Error in (Multi)linear Regression
- WWGD
- · Replies 3 ·
Finding eigenvalues and eigenvectors for a 2×2 matrix
- wefweff
- · Replies 1 ·
Graduate Infinite-Dimensional Lie Algebra
- fresh_42
- · Replies 4 ·
System of Equations for Second-Order IVP
- karush
- · Replies 4 ·
097 Change the second-order IVP into a system of equations
- karush
- · Replies 7 ·
Undergrad Change-of-basis matrix vs linear transformation in same basis
- fog37
- · Replies 12 ·
Solving Matrix A: Characteristic Equation and Eigenvectors
- wefweff
- · Replies 2 ·
Undergrad Reducing NxN Matrix to 2x2 w/ Physical Constraints
- waynewec
- · Replies 3 ·
Undergrad Theory of Schemes in Algebraic Geometry
- dx
- · Replies 14 ·
Λ and μ are scalars, find the value of λ and the value of μ
- Help seeker
- · Replies 4 ·
Graduate How to Solve B^3 = A^2 Matrix 2x2 on C?
- maria papadakh
- · Replies 11 ·
Undergrad Determine if polynomial system has finite number of solutions
- aheight
- · Replies 6 ·
Undergrad Solving a constraint on sensor array weights for omnidirectional patterns
- marcusl
- · Replies 5 ·
Graduate Understanding of conjugate directions
- Ironphys
- · Replies 1 ·
Undergrad Weird Semidirect Product Formula
- jstrunk
- · Replies 3 ·
Undergrad Determining the number of conjugacy classes in a p-group
- jstrunk
- · Replies 6 ·
5.2a plot linear transformations
- karush
- · Replies 2 ·
Undergrad Can a group be isomorphic to one of its quotients?
- WWGD
- · Replies 4 ·
High School Giving definitions, proposing theorems in abstract spaces
- trees and plants
- · Replies 10 ·
072 is Q(theta) a linear transformation from R^2 to itself.
- karush
- · Replies 4 ·
Undergrad When is it better to call a thing "modulus" and when "determinant"?
- Anixx
- · Replies 19 ·
Proving det(αA) = α^n det(A) for scalar multiplication
- karush
- · Replies 2 ·
Graduate Translationlength by the coxeterelement of E9 along the coxeteraxis
- reinhard55
- · Replies 9 ·
Undergrad Permutations written as product of 2-cycles
- Kaguro
- · Replies 4 ·
Construct matrices whose null space is span of given vector
- karush
- · Replies 3 ·
Whit.a.6.1 Show that the plane H defined by:
- karush
- · Replies 3 ·
051 how they got the eigenspaces ?
- karush
- · Replies 2 ·
Undergrad The adjective "finite" applied to algebraic structures
- Stephen Tashi
- · Replies 4 ·
Undergrad General worked out solution for diagonalizing a 4x4 Hermitian matrix
- Amentia
- · Replies 6 ·
Q01 are linearly independent vectors, so are....
- karush
- · Replies 1 ·