Linear and Abstract Algebra Forum

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.

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Undergrad Determinant and linear-algebraic aspects of Sudoku puzzles

  • WWGD
  • · Replies 7 ·
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Undergrad How to Show U|v⟩ = e^(ia)|v⟩ for Unitary Operators?

  • Peter_Newman
  • · Replies 12 ·
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12

Undergrad Proving ##\partial^{i} = g^{ik} \partial_{k}##

  • SplinterCell
  • · Replies 8 ·
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8

Undergrad Why are determinants in 2x2 matrices and 3x3 matrices computed the way they are?

  • Ale_Rodo
  • · Replies 13 ·
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Undergrad Why is gcd(x,n) either n or p when p divides x and n=pq?

  • Peter_Newman
  • · Replies 8 ·
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8

Undergrad I think I've hit upon a very easy proof of impossibility of quintic

  • swampwiz
  • · Replies 2 ·
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2

Matrix Transforms: nxm, n->m, m->n, n+m->n/m

  • Imiebee
  • · Replies 3 ·
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Undergrad The tensor product of tensors confusion

  • GR191511
  • · Replies 32 ·
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32

High School Is it invalid to redefine the sgn function in this way in a proof?

  • Eclair_de_XII
  • · Replies 15 ·
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High School Solutions for universal linear recursions

  • coolul007
  • · Replies 7 ·
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7

Graduate Center of a linear algebraic group

  • fresh_42
  • · Replies 9 ·
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9

High School Proving the uniqueness of eigenspaces

  • Eclair_de_XII
  • · Replies 6 ·
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QR decomposition with permutation matrix

  • mathmari
  • · Replies 6 ·
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Approximation of eigenvalue with inverse iteration method

  • mathmari
  • · Replies 2 ·
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Scalar Triple Product and Coplanarity

  • brinlin
  • · Replies 3 ·
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3

Householder method : Which α do we take?

  • mathmari
  • · Replies 4 ·
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4

Undergrad Central Extension and Cohomology Groups

  • giulio_hep
  • · Replies 7 ·
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Undergrad Prove that the limit of this matrix expression is 0

  • lriuui0x0
  • · Replies 5 ·
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5

High School Any square matrix can be expressed as the sum of anti/symmetric matrices

  • Eclair_de_XII
  • · Replies 7 ·
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High School Geometrical meaning of magnitude of vector product

  • songoku
  • · Replies 9 ·
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9

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
  • · Replies 3 ·
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3

Graduate Link between 24 dimension kissing number and Monster group

  • Labyrinth
  • · Replies 7 ·
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7

Undergrad How to Find the Generalized Eigenvector in a Matrix ODE?

  • Alwar
  • · Replies 10 ·
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10

Examples of vector spaces over different fields

  • nweissma
  • · Replies 1 ·
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Proving Non-Degeneracy of Euclidean Inner Products

  • steenis
  • · Replies 8 ·
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8

Graduate A problem in multilinear algebra

  • steenis
  • · Replies 2 ·
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2

High School Regarding Contravarient Vector Transformations

  • AdvaitDhingra
  • · Replies 25 ·
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25

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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8

Understanding Velocity and Acceleration of a Moving Particle

  • WMDhamnekar
  • · Replies 2 ·
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Undergrad Shouldn't this definition of a metric include a square root?

  • nomadreid
  • · Replies 8 ·
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8

How is Radius of Curvature Computed for a Given Curve?

  • WMDhamnekar
  • · Replies 2 ·
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2

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
  • · Replies 6 ·
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Undergrad Why pairwise intersections don't define direct sums of three subspaces

  • JD_PM
  • · Replies 7 ·
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7

Diagonalizable transformation - Existence of basis

  • mathmari
  • · Replies 52 ·
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Undergrad How to show span(U₁∪...∪Uₖ₋₁) + Uₖ = span(U₁∪...∪Uₖ)

  • JD_PM
  • · Replies 10 ·
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10

Is the Matrix A Diagonalizable with Real Eigenvalues?

  • mathmari
  • · Replies 10 ·
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High School Commutators of functions of operators

  • LagrangeEuler
  • · Replies 2 ·
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Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?

  • karush
  • · Replies 2 ·
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Undergrad Meaning of terms in a direct sum decomposition of an algebra

  • Rabindranath
  • · Replies 8 ·
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8

Graduate Lie Bracket * Matrix * vector (Need proof)

  • Trying2Learn
  • · Replies 9 ·
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9

What is the velocity vector after a pinball bounces off a baffle?

  • WMDhamnekar
  • · Replies 4 ·
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4

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
  • · Replies 1 ·
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Prove $10^{\dfrac{5^n -1}{4}} \Huge\vert (5^n)!$ for $Z^+$

  • karush
  • · Replies 6 ·
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6

Undergrad Canonical Form for quadratic equations *with* linear terms

  • arestes
  • · Replies 4 ·
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4

Undergrad Two ways to define operations in a vector space

  • Santiago24
  • · Replies 7 ·
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7

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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6

Find the elementary divisors and invariant factors

  • fabiancillo
  • · Replies 2 ·
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Undergrad How can the Lp Norm be used to prove inequalities?

  • ashah99
  • · Replies 9 ·
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5

The product γ is a rotation or a translation

  • mathmari
  • · Replies 11 ·
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11

What are the properties of affine bases in $\mathbb{R}^n$?

  • mathmari
  • · Replies 15 ·
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15

Checking if $\beta \in \text{Isom}(\mathbb{R}^2)$

  • mathmari
  • · Replies 15 ·
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15

Graduate Multinomial functions of matrices

  • Stephen Tashi
  • · Replies 3 ·
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3

Set of 2-dimensional orthogonal matrices equal to an union of sets

  • mathmari
  • · Replies 9 ·
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9

Graduate Trace of the inverse of matrix products

  • nikozm
  • · Replies 2 ·
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Undergrad What conditions are needed to raise a linear operator to some power?

  • fxdung
  • · Replies 4 ·
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4

Undergrad Commutative algebra and differential geometry

  • dx
  • · Replies 3 ·
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3

High School Explicit expression for ideal membership

  • aheight
  • · Replies 3 ·
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3

Hectares and kilometres - how many days to cut 295 hectares

  • Kzerr
  • · Replies 3 ·
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Undergrad One-Time Pad and Frequency Analysis

  • Haku
  • · Replies 16 ·
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16

3.2.5.3 General Solution if system

  • karush
  • · Replies 14 ·
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14

Solving 2nd-Order IVP as System of Equations

  • karush
  • · Replies 2 ·
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2

Graduate Error in (Multi)linear Regression

  • WWGD
  • · Replies 3 ·
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3

Finding eigenvalues and eigenvectors for a 2×2 matrix

  • wefweff
  • · Replies 1 ·
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1

Graduate Infinite-Dimensional Lie Algebra

  • fresh_42
  • · Replies 4 ·
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4

System of Equations for Second-Order IVP

  • karush
  • · Replies 4 ·
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4

097 Change the second-order IVP into a system of equations

  • karush
  • · Replies 7 ·
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7

Undergrad Change-of-basis matrix vs linear transformation in same basis

  • fog37
  • · Replies 12 ·
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12

Solving Matrix A: Characteristic Equation and Eigenvectors

  • wefweff
  • · Replies 2 ·
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2

Undergrad Reducing NxN Matrix to 2x2 w/ Physical Constraints

  • waynewec
  • · Replies 3 ·
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3

Undergrad Theory of Schemes in Algebraic Geometry

  • dx
  • · Replies 14 ·
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14

Λ and μ are scalars, find the value of λ and the value of μ

  • Help seeker
  • · Replies 4 ·
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4

Graduate How to Solve B^3 = A^2 Matrix 2x2 on C?

  • maria papadakh
  • · Replies 11 ·
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11

Undergrad Determine if polynomial system has finite number of solutions

  • aheight
  • · Replies 6 ·
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6

Undergrad Solving a constraint on sensor array weights for omnidirectional patterns

  • marcusl
  • · Replies 5 ·
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5

Graduate Understanding of conjugate directions

  • Ironphys
  • · Replies 1 ·
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Undergrad Weird Semidirect Product Formula

  • jstrunk
  • · Replies 3 ·
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3

Undergrad Determining the number of conjugacy classes in a p-group

  • jstrunk
  • · Replies 6 ·
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5.2a plot linear transformations

  • karush
  • · Replies 2 ·
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Undergrad Can a group be isomorphic to one of its quotients?

  • WWGD
  • · Replies 4 ·
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High School Giving definitions, proposing theorems in abstract spaces

  • trees and plants
  • · Replies 10 ·
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072 is Q(theta) a linear transformation from R^2 to itself.

  • karush
  • · Replies 4 ·
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Undergrad When is it better to call a thing "modulus" and when "determinant"?

  • Anixx
  • · Replies 19 ·
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19

Proving det(αA) = α^n det(A) for scalar multiplication

  • karush
  • · Replies 2 ·
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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
  • · Replies 4 ·
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4

Construct matrices whose null space is span of given vector

  • karush
  • · Replies 3 ·
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Whit.a.6.1 Show that the plane H defined by:

  • karush
  • · Replies 3 ·
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051 how they got the eigenspaces ?

  • karush
  • · Replies 2 ·
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Undergrad The adjective "finite" applied to algebraic structures

  • Stephen Tashi
  • · Replies 4 ·
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4

Undergrad General worked out solution for diagonalizing a 4x4 Hermitian matrix

  • Amentia
  • · Replies 6 ·
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6

Q01 are linearly independent vectors, so are....

  • karush
  • · Replies 1 ·
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