Linear and Abstract Algebra Forum

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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.
Undergrad How to Show U|v⟩ = e^(ia)|v⟩ for Unitary Operators?
  • Peter_Newman
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Undergrad Proving ##\partial^{i} = g^{ik} \partial_{k}##
  • SplinterCell
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Undergrad Why are determinants in 2x2 matrices and 3x3 matrices computed the way they are?
  • Ale_Rodo
  • · Replies 13 ·
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Undergrad Understanding the Results of gcd(x,n)
  • Peter_Newman
  • · Replies 8 ·
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Undergrad I think I've hit upon a very easy proof of impossibility of quintic
  • swampwiz
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Matrix Transforms: nxm, n->m, m->n, n+m->n/m
  • Imiebee
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Undergrad The tensor product of tensors confusion
  • GR191511
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High School Is it invalid to redefine the sgn function in this way in a proof?
  • Eclair_de_XII
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High School What Are Solutions for Universal Linear Recursions?
  • coolul007
  • · Replies 7 ·
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Graduate Center of a linear algebraic group
  • fresh_42
  • · Replies 9 ·
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High School Proving the uniqueness of eigenspaces
  • Eclair_de_XII
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QR decomposition with permutation matrix
  • mathmari
  • · Replies 6 ·
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Approximation of eigenvalue with inverse iteration method
  • mathmari
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Scalar Triple Product and Coplanarity
  • brinlin
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Householder method : Which α do we take?
  • mathmari
  • · Replies 4 ·
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Undergrad Central Extension and Cohomology Groups
  • giulio_hep
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Undergrad Prove that the limit of this matrix expression is 0
  • lriuui0x0
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High School Any square matrix can be expressed as the sum of anti/symmetric matrices
  • Eclair_de_XII
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High School Geometrical meaning of magnitude of vector product
  • songoku
  • · Replies 9 ·
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Find Vector of Given Length in Particular Direction
  • brinlin
  • · Replies 1 ·
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What is the Angle Between Vectors Using the Dot Product Formula?
  • brinlin
  • · Replies 4 ·
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Find Vector Perpendicular to Plane
  • brinlin
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Graduate Link between 24 dimension kissing number and Monster group
  • Labyrinth
  • · Replies 7 ·
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Undergrad How to Find the Generalized Eigenvector in a Matrix ODE?
  • Alwar
  • · Replies 10 ·
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Abstract algebra: i need examples of ...
  • nweissma
  • · Replies 1 ·
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Proving Non-Degeneracy of Euclidean Inner Products
  • steenis
  • · Replies 8 ·
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Graduate A problem in multilinear algebra
  • steenis
  • · Replies 2 ·
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High School Regarding Contravarient Vector Transformations
  • AdvaitDhingra
  • · Replies 25 ·
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Undergrad Proving (x,x) = 0 implies x = 0 in real vector space V
  • steenis
  • · Replies 21 ·
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Velocity and acceleration vectors and their magnitudes
  • WMDhamnekar
  • · Replies 8 ·
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Understanding Velocity and Acceleration of a Moving Particle
  • WMDhamnekar
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Undergrad Shouldn't this definition of a metric include a square root?
  • nomadreid
  • · Replies 8 ·
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How is Radius of Curvature Computed for a Given Curve?
  • WMDhamnekar
  • · Replies 2 ·
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Prove R is a Sub-ring of $\mathbb{Q}$ - Prime $p \in \mathbb{Z}$
  • fabiancillo
  • · Replies 11 ·
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Undergrad Proving that ##V = U_1 \oplus U_2 \oplus \ldots \oplus U_k##
  • JD_PM
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Undergrad Understanding the concept of direct sum
  • JD_PM
  • · Replies 7 ·
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Diagonalizable transformation - Existence of basis
  • mathmari
  • · Replies 52 ·
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Undergrad Proving U_1 + U_2 + ... + U_k = span (U_1 \cup U_2 \cup \ ... \ \cup U_k)
  • JD_PM
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Is the Matrix A Diagonalizable with Real Eigenvalues?
  • mathmari
  • · Replies 10 ·
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High School Commutators of functions of operators
  • LagrangeEuler
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Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
  • karush
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Undergrad Meaning of terms in a direct sum decomposition of an algebra
  • Rabindranath
  • · Replies 8 ·
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Graduate Lie Bracket * Matrix * vector (Need proof)
  • Trying2Learn
  • · Replies 9 ·
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What is the velocity vector after a pinball bounces off a baffle?
  • WMDhamnekar
  • · Replies 4 ·
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Undergrad How is unit norm axis rotation represented and derived in R3?
  • LCSphysicist
  • · Replies 4 ·
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Undergrad Dimension of a Linear Transformation Matrix
  • patric44
  • · Replies 4 ·
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Is the Calculated Osculating Plane and Binormal Correct for $\theta=0$?
  • WMDhamnekar
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Prove $10^{\dfrac{5^n -1}{4}} \Huge\vert (5^n)!$ for $Z^+$
  • karush
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Undergrad Canonical Form for quadratic equations *with* linear terms
  • arestes
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Undergrad Two ways to define operations in a vector space
  • Santiago24
  • · Replies 7 ·
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Undergrad Un-skewing a skew symmetric matrix (for want of a better phrase)
  • Trying2Learn
  • · Replies 1 ·
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High School Magnitudes of the sum of two vectors
  • keroberous
  • · Replies 6 ·
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Find the elementary divisors and invariant factors
  • fabiancillo
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Undergrad How can the Lp Norm be used to prove inequalities?
  • ashah99
  • · Replies 9 ·
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Undergrad Question about the vector cross product in spherical or cylindrical coordinates
  • dyn
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The product γ is a rotation or a translation
  • mathmari
  • · Replies 11 ·
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What are the properties of affine bases in $\mathbb{R}^n$?
  • mathmari
  • · Replies 15 ·
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Checking if $\beta \in \text{Isom}(\mathbb{R}^2)$
  • mathmari
  • · Replies 15 ·
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Graduate Multinomial functions of matrices
  • Stephen Tashi
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Set of 2-dimensional orthogonal matrices equal to an union of sets
  • mathmari
  • · Replies 9 ·
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Graduate Trace of the inverse of matrix products
  • nikozm
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Undergrad What conditions are needed to raise a linear operator to some power?
  • fxdung
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Undergrad Commutative algebra and differential geometry
  • dx
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High School Explicit expression for ideal membership
  • aheight
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Hectares and kilometres - how many days to cut 295 hectares
  • Kzerr
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Undergrad One-Time Pad and Frequency Analysis
  • Haku
  • · Replies 16 ·
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3.2.5.3 General Solution if system
  • karush
  • · Replies 14 ·
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Solving 2nd-Order IVP as System of Equations
  • karush
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Graduate Error in (Multi)linear Regression
  • WWGD
  • · Replies 3 ·
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Find Eigenvalues & Basis C2 Matrix: Help!
  • wefweff
  • · Replies 1 ·
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Graduate Infinite-Dimensional Lie Algebra
  • fresh_42
  • · Replies 4 ·
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System of Equations for Second-Order IVP
  • karush
  • · Replies 4 ·
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097 Change the second-order IVP into a system of equations
  • karush
  • · Replies 7 ·
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Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
  • fog37
  • · Replies 12 ·
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Solving Matrix A: Characteristic Equation and Eigenvectors
  • wefweff
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Undergrad Reducing NxN Matrix to 2x2 w/ Physical Constraints
  • waynewec
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Undergrad Theory of Schemes in Algebraic Geometry
  • dx
  • · Replies 14 ·
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Λ and μ are scalars, find the value of λ and the value of μ
  • Help seeker
  • · Replies 4 ·
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Graduate How to Solve B^3 = A^2 Matrix 2x2 on C?
  • maria papadakh
  • · Replies 11 ·
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Undergrad Determine if polynomial system has finite number of solutions
  • aheight
  • · Replies 6 ·
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Undergrad Help solving a System of Linear Equations
  • marcusl
  • · Replies 5 ·
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Graduate Understanding of conjugate directions
  • Ironphys
  • · Replies 1 ·
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Undergrad Weird Semidirect Product Formula
  • jstrunk
  • · Replies 3 ·
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Undergrad Determining the number of conjugacy classes in a p-group
  • jstrunk
  • · Replies 6 ·
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5.2a plot linear transformations
  • karush
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Undergrad Can a group be isomorphic to one of its quotients?
  • WWGD
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High School Giving definitions, proposing theorems in abstract spaces
  • trees and plants
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072 is Q(theta) a linear transformation from R^2 to itself.
  • karush
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Undergrad When is it better to call a thing "modulus" and when "determinant"?
  • Anixx
  • · Replies 19 ·
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T20 Suppose that A is a square matrix of size n and ......
  • karush
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Graduate Translationlength by the coxeterelement of E9 along the coxeteraxis
  • reinhard55
  • · Replies 9 ·
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Undergrad Permutations written as product of 2-cycles
  • Kaguro
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Matrices.......whose null space consists all linear combinations
  • karush
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Whit.a.6.1 Show that the plane H defined by:
  • karush
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051 how they got the eigenspaces ?
  • karush
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Undergrad The adjective "finite" applied to algebraic structures
  • Stephen Tashi
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Undergrad General worked out solution for diagonalizing a 4x4 Hermitian matrix
  • Amentia
  • · Replies 6 ·
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Q01 are linearly independent vectors, so are....
  • karush
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Graduate What physical meaning can the “determinant” of a divergency have?
  • Anixx
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Give a basis to get the specific matrix M
  • mathmari
  • · Replies 34 ·
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