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.

Threads

Graduate Isomorphism between M × M and R²

  • alexbennie
  • · Replies 2 ·
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2

Factoring RSA-200

  • Zurtex
  • · Replies 13 ·
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13

Undergrad Prove A is invertible iff A^T*A is invertible

  • physicsss
  • · Replies 5 ·
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5

Graduate Can An Infinite Power Set Be Defined and Is it a Set?

  • Don Aman
  • · Replies 3 ·
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3

Undergrad Abstract Algebra book suggestions

  • Karate Chop
  • · Replies 18 ·
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18

Graduate Proof of Golbach's conjecture and the twin prime conjecture

  • keebs
  • · Replies 9 ·
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9

Graduate Congruence Problem Solution for FLT

  • vantheman
  • · Replies 19 ·
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19

Graduate Proving solvability of y² + p² = 2x² from related Diophantine equations

  • angelo
  • · Replies 4 ·
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4

Graduate Does Deutsch's algorithm reveal insights into prime density?

  • Loren Booda
  • · Replies 5 ·
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5

Undergrad Orthonormal, Orthogonal, Perpendicular

  • Nusc
  • · Replies 4 ·
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4

Graduate Is Ker(f)={e} Enough to Prove Injectivity for a Group Homomorphism?

  • quasar987
  • · Replies 67 ·
3
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67

Graduate Can Linear Independence of Vector Pairs Imply Independence of Their Union?

  • physicsss
  • · Replies 3 ·
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3

Undergrad Sin(2x) and sin(3x) are orthogonal to each other

  • SSSUNNN
  • · Replies 4 ·
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4

Graduate What is the basis for the subspace W spanned by {sin^2(x), cos^2(x), cos2x}?

  • physicsss
  • · Replies 4 ·
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4

Graduate How Can I Decompose a 3x3 Rotation Matrix into a Product of 3 Rotations?

  • Cristi-Tota
  • · Replies 1 ·
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1

High School Matrices in more than 2 dimensions

  • The Rev
  • · Replies 5 ·
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5

Undergrad MinimalPolynomial.pdfHow Can I Find the Minimal Polynomial for a Given Matrix A?

  • Chen
  • · Replies 2 ·
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2

Undergrad Span of (1,1,1) and (1,-1,1) in R^3

  • physicsss
  • · Replies 6 ·
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6

Graduate Constructing a Cartesian Closed Topos for Real Closed Fields

  • Hurkyl
  • · Replies 2 ·
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2

Graduate Transpose of Matrix as Linear Map

  • chingkui
  • · Replies 2 ·
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2

Graduate Proof of $(I-C)^{-1}\leq \|I\| + \|C\| + \|C\|^2 + \cdots$ Using Matrix C

  • flop
  • · Replies 2 ·
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2

Undergrad Prove 3 divides n³ - 7n + 3 by induction

  • johnnyICON
  • · Replies 8 ·
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8

Graduate Finding Eigenvectors for Coordinate transformation

  • pjg
  • · Replies 11 ·
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11

Undergrad Is scalar multiplication to zero a valid vector space operation?

  • physicsss
  • · Replies 13 ·
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13

Graduate Complex roots problem (a proof by induction)

  • TomMe
  • · Replies 12 ·
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12

Undergrad Linear and Abstract Algebra textbooks

  • Icebreaker
  • · Replies 48 ·
2
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48

Graduate Alsings hypothesis of integers bigger than 2

  • HAP
  • · Replies 2 ·
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2

Undergrad Solving 4x4 Determinant - Find a and b

  • cnky
  • · Replies 8 ·
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8

Undergrad Is Sudoku Addicting and Mathematically Complex?

  • quetzalcoatl9
  • · Replies 2 ·
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2

Undergrad Finding a Basis for M2's Symmetric Matrices

  • heman
  • · Replies 3 ·
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3

Undergrad Solving 10cos(x) + 13.41cos(y) = 5.4 with constraint

  • John O' Meara
  • · Replies 2 ·
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2

High School Why is gcd important in number theory?

  • honestrosewater
  • · Replies 21 ·
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21

Undergrad Does the notation used for the span part of an eigenvector matter?

  • amcavoy
  • · Replies 2 ·
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2

Graduate Natural isomorphism of VxV* and End(V)

  • Don Aman
  • · Replies 22 ·
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22

Graduate Groups of Even Order Containing Odd Number of Elements of Order 2

  • quasar987
  • · Replies 19 ·
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19

Graduate Curious about a pattern to prime products.

  • rshriner
  • · Replies 13 ·
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13

Graduate Equivalent conditions for hermitian matrix

  • twoflower
  • · Replies 5 ·
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5

Graduate Asymptotic formula for Mertens function

  • keebs
  • · Replies 4 ·
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4

Undergrad How to find all solutions of Pell equation

  • murshid_islam
  • · Replies 14 ·
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14

Graduate Something about hermitian matrixes

  • twoflower
  • · Replies 5 ·
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5

Undergrad Kernel of differentiation and integration

  • madking153
  • · Replies 5 ·
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5

Undergrad Prove that if n divides a - b, then n divides a and b

  • quasar987
  • · Replies 29 ·
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29

Undergrad A simple permutation question or not so simple

  • johnnyICON
  • · Replies 9 ·
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9

Graduate Sum of quadratic residues modulo a prime

  • T.Rex
  • · Replies 5 ·
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5

Graduate What is the Identity Property of Determinants and its Relation to Linearity?

  • twoflower
  • · Replies 4 ·
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4

Undergrad How Is the Vector Solution 1/2(p-q) Derived?

  • m00c0w
  • · Replies 3 ·
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3

Undergrad Nontrivial Subspace with Equal Dimensions: Linear Algebra Example

  • dan0
  • · Replies 2 ·
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2

Graduate Can a group of order 98 have a subgroup of order 7?

  • rayveldkamp
  • · Replies 2 ·
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2

Graduate Does every polynomial over integers split over some finite field?

  • snoble
  • · Replies 13 ·
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13

Graduate Final Physics Degree: What Are Quaternion Math Problems Used For?

  • James Jackson
  • · Replies 2 ·
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2

Graduate Something that's been frustrating me

  • Manchot
  • · Replies 4 ·
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4

High School 0/0 Anything divided by zero is undefined

  • madness
  • · Replies 11 ·
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11

Undergrad Complex conjugate of a 5 x 5 matrices?

  • ayalam
  • · Replies 7 ·
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7

Undergrad How Can a Physics Student Self-Learn Linear Algebra?

  • Baggio
  • · Replies 8 ·
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8

Graduate Proving the Convergence of a Sequence Defined by Induction

  • johnnyICON
  • · Replies 8 ·
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8

High School How can 2D planes exist without thickness in real space?

  • DOCMUR
  • · Replies 3 ·
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3

Undergrad How Can I Determine if a Matrix is Positive?

  • Seckin Sefi
  • · Replies 2 ·
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2

Graduate Show that a weighted integral defines an inner product on ℝ₁[x]

  • Zurtex
  • · Replies 17 ·
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17

Undergrad Theorem regarding mod properties

  • plusunim
  • · Replies 5 ·
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5

Graduate Linear algebra proofs on identity operators, similarity, and eigenvalues

  • hola
  • · Replies 20 ·
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20

Graduate Proving Orthogonality of Non-Zero Vectors

  • mattmns
  • · Replies 13 ·
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13

Undergrad Help with linear algebra final: eigenvalues, eigenvectors, diagonalization

  • Gale
  • · Replies 26 ·
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26

Graduate Let V be a 5 dimensional vector space

  • laminatedevildoll
  • · Replies 2 ·
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2

Graduate What progress has been made on the Riemann Hypothesis since 2004?

  • Icebreaker
  • · Replies 2 ·
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2

Undergrad Markov chains and steady state vectors

  • Physics is Phun
  • · Replies 3 ·
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3

Graduate Proving Solutions of Linear Transformations Using Kernel and Fixed Vectors

  • laminatedevildoll
  • · Replies 4 ·
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4

Undergrad Understanding Right and Left Handed Systems in Vector Calculus

  • laminatedevildoll
  • · Replies 2 ·
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2

Graduate What's the probability of R in C?

  • Sabine
  • · Replies 12 ·
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12

Graduate Can a subspace be written as the direct sum of two orthogonal spaces?

  • matness
  • · Replies 11 ·
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11

Undergrad Proving a number is divisible by 48

  • johnnyICON
  • · Replies 33 ·
2
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33

Undergrad Do Infinitely Many Prime Pairs Exist?

  • nnnnnnnn
  • · Replies 93 ·
4
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93

Graduate Show Reducibility of x^4+1 Modulo p

  • Palindrom
  • · Replies 11 ·
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11

High School Is Zero Raised to the Power of Zero Equal to One?

  • The Rev
  • · Replies 83 ·
3
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83

Undergrad Prove gcd(b, d) = gcd(a, b) when d = a + bc

  • BicycleTree
  • · Replies 11 ·
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11

Graduate Does the axiom of choice guarantee a basis for every vector space?

  • chingkui
  • · Replies 15 ·
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15

Graduate Eigenvalues, eigenvectors question

  • jhson114
  • · Replies 4 ·
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4

Graduate What is the difference between diagonal form and Dirac form of an operator?

  • James Jackson
  • · Replies 2 ·
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2

Undergrad Order of operations in modular arithmetic with exponents

  • johnnyICON
  • · Replies 8 ·
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8

Undergrad Determinants of odd skew-symmetric matrices and eigenvalues of inverses

  • jhson114
  • · Replies 15 ·
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15

Graduate Powers of a non-diagonalizable matrix?

  • TomMe
  • · Replies 6 ·
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6

High School What is the Fibonacci sequence?

  • Leopold Infeld
  • · Replies 6 ·
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6

Graduate Is the polar vector E a basis for a representation of group Oh?

  • PhysKid24
  • · Replies 3 ·
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3

Undergrad Verify Linear Transformations: 3.4a, 3.4b

  • laminatedevildoll
  • · Replies 2 ·
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2

High School Understanding Congruency and Its Applications

  • johnnyICON
  • · Replies 3 ·
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3

High School Where Can I Find a Base to Base Conversion Calculator for Various Number Bases?

  • RandallB
  • · Replies 2 ·
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2

Graduate What Are the Clues for Proving the Eigenvalue Equation in Physics?

  • quasar987
  • · Replies 14 ·
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14

Undergrad How much commutativity in associativity

  • Kocur
  • · Replies 9 ·
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9

Graduate What Defines Mainvectors in the Context of Eigenvalue Multiplicities?

  • yeus
  • · Replies 3 ·
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3

Undergrad Is Infinity Just an Inverse Zero?

  • Coqui
  • · Replies 6 ·
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6

Solving a Problem: Seeking Feedback

  • laminatedevildoll
  • · Replies 2 ·
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2

High School Is Subtraction of Real Numbers Associative or Not?

  • Kocur
  • · Replies 3 ·
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3

Graduate Proof Hint: Show +-1 are Eigenvalues of T on nxn Matrices with Real Entries

  • eckiller
  • · Replies 2 ·
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2

Graduate Defining polar coordinates without undefined tangent values

  • quasar987
  • · Replies 10 ·
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10

Undergrad Little excercise about bases (question)

  • TomMe
  • · Replies 16 ·
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16

Undergrad Cross product of polar coordinates

  • tiagobt
  • · Replies 2 ·
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2

Undergrad Does a 2×3 matrix span ℝ² using the given theorem?

  • Mathman23
  • · Replies 2 ·
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2

Graduate Prime Numbers in the Diophantine equation q=(n^2+1)/p and p is Prime

  • AntonVrba
  • · Replies 5 ·
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5

Undergrad If B²=B, prove det(B)=1 or B is singular

  • hola
  • · Replies 7 ·
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7

Undergrad Number theory notes from Cambridge first year syllabus

  • maverickmathematics
  • · Replies 6 ·
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6

Graduate Free algebra notes on linear algebra, group theory, Riemann-Roch

  • mathwonk
  • · Replies 17 ·
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17