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 Can a non-symmetric matrix be positive definite?

  • Leo321
  • · Replies 5 ·
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5

Graduate Why does λ divide one of x, y, z in the equation x³ + y³ = z³?

  • Brimley
  • · Replies 2 ·
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2

Undergrad Matrix of order supose 3*3 is in span of R3

  • asad khan
  • · Replies 2 ·
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2

Undergrad Frequency of Greatest Integer quotients

  • jleach
  • · Replies 4 ·
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4

Graduate What is the orbit of 1 in the permutation group G?

  • mathplease
  • · Replies 4 ·
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4

Undergrad Fortran Code for Solving Linear System w/ Least Square Method

  • passionfly
  • · Replies 1 ·
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1

Undergrad Matrices with all zero eigenvalues

  • Leo321
  • · Replies 5 ·
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5

Undergrad What Does F Represent in Group Theory?

  • MikeDietrich
  • · Replies 2 ·
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2

High School Set of linear equations and simultaneous linear equations

  • nobahar
  • · Replies 4 ·
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4

Undergrad Solve Equation: 3^x-2^y=1 - Positive Integer Solutions

  • 511201
  • · Replies 1 ·
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1

Undergrad Properties of systems of linear equations

  • hholzer
  • · Replies 2 ·
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2

Undergrad How to find detA if A is 4X4 matrix

  • ranoo
  • · Replies 7 ·
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7

Graduate Solutions of an equation in a PID

  • ihggin
  • · Replies 1 ·
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1

Graduate Finite Subsets of N: Proving Countability

  • kingtaf
  • · Replies 3 ·
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3

Undergrad Can S5 contain a subgroup of order 7?

  • eileen6a
  • · Replies 3 ·
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3

Graduate How do you define congruence modulo a quadratic integer in Q[sqrt(-d)]?

  • Brimley
  • · Replies 23 ·
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23

Undergrad What vector space contains the span of cos x and sin x?

  • ask_LXXXVI
  • · Replies 8 ·
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8

Graduate Proof involving surjective/onto and image/preimage of sets

  • mathmajor2013
  • · Replies 1 ·
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1

Graduate A group of finite order can be infinitely large?

  • jessicaw
  • · Replies 5 ·
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5

Undergrad What is the relationship between a matrix and its transpose in linear algebra?

  • matqkks
  • · Replies 1 ·
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1

Graduate Finite field is algebraically closed under constraint?

  • gepolv
  • · Replies 1 ·
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1

Graduate Prime Factorial Proof: Existence of a Prime Between n and n!

  • kingtaf
  • · Replies 7 ·
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7

Graduate Showing Gal(E/Q) is Isomorphic to Z4

  • algekkk
  • · Replies 4 ·
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4

Graduate Simple Rings: Commutativity and Identity

  • jem05
  • · Replies 9 ·
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9

Graduate Prove Symmetry Group of Regular Polygon Has 1 & 2 Dim Irreducible Reps

  • wdlang
  • · Replies 4 ·
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4

Graduate Lie Algebra differentiable manifold

  • Hymne
  • · Replies 1 ·
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1

Undergrad What really is a group in abstract algebra?

  • Grouphelp
  • · Replies 6 ·
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6

Graduate How to prove the order of x,y in this case

  • ranoo
  • · Replies 2 ·
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2

Graduate Does positive-definite order imply determinant order?

  • hadron23
  • · Replies 2 ·
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2

Undergrad Why is every linear transformation from Rn to Rm a matrix transformation?

  • finkeljo
  • · Replies 2 ·
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2

Undergrad Why Do Irrational Numbers Exist?

  • timjones007
  • · Replies 73 ·
3
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73

Undergrad How Does Squaring a Matrix Affect Its Determinant?

  • chapone
  • · Replies 9 ·
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9

Graduate How does exp relate a Lie group to its Lie algebra?

  • geodesic42
  • · Replies 12 ·
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12

Undergrad Why linear independence alone proves a basis in finite-dimensional spaces

  • Bachelier
  • · Replies 9 ·
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9

Graduate Prime values of integer polynomials

  • VKint
  • · Replies 3 ·
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3

Undergrad Factoring N=pq when only the last digits of p and q are known

  • epsi00
  • · Replies 1 ·
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1

Graduate Why aren't the integers of Q[√−5] a UFD?

  • Brimley
  • · Replies 9 ·
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9

Graduate What is the Difference Between Factor Space and Equivalence Classes?

  • commutator
  • · Replies 1 ·
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1

Graduate Do force and displacement exist in different vector spaces with multiple duals?

  • Rasalhague
  • · Replies 9 ·
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9

Undergrad How to prove that a set is a group? related difficult/challenge quesyion.

  • jessicaw
  • · Replies 6 ·
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6

Graduate Playing with Small Natural Numbers Network

  • networks
  • · Replies 3 ·
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3

Graduate Derivative of a function with matrices

  • Leo321
  • · Replies 10 ·
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10

Graduate Proving Congruence Classes in Q[√-3] with Prime Divisor λ

  • Brimley
  • · Replies 9 ·
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9

Graduate Is there a probabilistic approach to number theory conjectures?

  • arivero
  • · Replies 8 ·
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8

High School Adding 3.6, 4.4, and 5.8: Keeping the Sum 13.8

  • Frank66
  • · Replies 1 ·
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1

Undergrad Projecting a vector onto a plane problem

  • dcl
  • · Replies 4 ·
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4

Undergrad Tensor Analysis and Linear Algebra, what's the difference

  • mahinda
  • · Replies 2 ·
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2

Graduate Existence of polynomial in R^2

  • ihggin
  • · Replies 1 ·
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1

Undergrad I've never felt dumber: me understand Fibonacci identity.

  • moe darklight
  • · Replies 2 ·
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2

Graduate Why C([0,1]) and C_{o} are not isomorphic?

  • pp007
  • · Replies 12 ·
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12

Graduate Understanding Associates and Norms in Algebraic Integers

  • Brimley
  • · Replies 20 ·
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20

Graduate Show one ring not isomorphic to the other

  • chycachrrycol
  • · Replies 1 ·
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1

Graduate All Eigenvalues Lie on the Unit Circle

  • ali987
  • · Replies 5 ·
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5

Undergrad Finding the General Term for Perfect Squares

  • sachinism
  • · Replies 2 ·
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2

Undergrad Finding coefficients to express arbitrary vectors as linear combinations

  • freshlikeuhh
  • · Replies 1 ·
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1

Graduate Find and Test Primes using the Chinese Remainder Theorem and Binary Search

  • John Creighto
  • · Replies 2 ·
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2

Graduate Why do Wikipedia and Mathworld define interior product differently?

  • Rasalhague
  • · Replies 3 ·
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3

Graduate Proof of Goldbach,Polignac,Legendre,Sophie Germain conjecture.pdf

  • choe
  • · Replies 2 ·
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2

Undergrad Why is 3AB+P Set to Zero in Cardan's Cubic Equation?

  • Physicsissuef
  • · Replies 3 ·
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3

High School How do I draw the vector A-3B+C in relation to like vectors?

  • tatiana
  • · Replies 1 ·
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1

Undergrad How Do These Linear Algebra Concepts Align with Definitions and Vector Spaces?

  • freshlikeuhh
  • · Replies 4 ·
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4

Undergrad How does this number system conversion algorithm work?

  • 0131313131313
  • · Replies 5 ·
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5

Graduate Irreducible Representations and Class

  • sineontheline
  • · Replies 1 ·
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1

High School What is the Best Way to Solve This Algebraic Brain Teaser?

  • cchave3
  • · Replies 3 ·
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3

Graduate Perron formula for matrix powers

  • bpet
  • · Replies 2 ·
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2

Graduate Nearest block diagonal matrix to a given matrix

  • cpp6f
  • · Replies 1 ·
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1

Graduate A More Abstract Definition of an Inner Product Space?

  • Laton
  • · Replies 17 ·
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17

Graduate Prove Minkowski Inequality using Cauchy-Schwartz Inequality

  • Rederick
  • · Replies 3 ·
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3

Graduate Eigen-vectors/values under row flipping

  • onako
  • · Replies 6 ·
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6

Graduate Is it possible to simplify the RH problem?

  • PeterJ
  • · Replies 15 ·
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15

Graduate Eisenstein's Irreducibility Criterion

  • roam
  • · Replies 10 ·
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10

Undergrad How Do You Prove This Linear Transformation?

  • ichigo444
  • · Replies 1 ·
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1

Graduate How to Find Subgroups of Index 2?

  • Newtime
  • · Replies 1 ·
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1

Graduate Infinitely many primes in Q[Sqrt(d)]

  • Brimley
  • · Replies 9 ·
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9

Graduate Pythagorean Theorem: Relationships in Euclidean Space

  • lavinia
  • · Replies 9 ·
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9

Undergrad Linear Combination: Can 1 0 1 0 be Combined?

  • ichigo444
  • · Replies 2 ·
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2

High School How do you multiply permutations?

  • JessBrown
  • · Replies 10 ·
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10

Graduate Is There a Simpler Way to Construct a Linear Functional Given a Linear Operator?

  • ihggin
  • · Replies 3 ·
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3

Graduate A very challenging question regarding in basic algebra group theory?

  • jessicaw
  • · Replies 2 ·
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2

Undergrad Invertability as a substitute for looking for linear independence

  • ichigo444
  • · Replies 3 ·
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3

Undergrad Linearly Dependent Sets: Answers to Your Questions

  • ichigo444
  • · Replies 3 ·
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3

Graduate Normed division algebras: geometrical limitation

  • BruceG
  • · Replies 2 ·
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2

Undergrad Largest determinant of a 3×3 matrix with 0/1 entries

  • neden
  • · Replies 3 ·
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3

Undergrad How to OLS several lines at once?

  • phrozenfearz
  • · Replies 2 ·
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2

Undergrad Proof that general solutions equal particular plus homogeneous solutions

  • miglo
  • · Replies 4 ·
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4

Graduate Find all roots of e^((π z)²) = i with |z| < 1

  • palaszz
  • · Replies 2 ·
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2

Undergrad Software that outputs a general polynomial formula for a finite series

  • Helicobacter
  • · Replies 6 ·
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6

Graduate Nonabelian group of order pq has a nonnormal subgroup

  • hermanni
  • · Replies 3 ·
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3

Graduate Are upper and lower triangular matrix groups isomorphic?

  • symbol0
  • · Replies 4 ·
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4

Undergrad Twin Prime Sieve: Calculate All Twins Less Than N - Todd's Version

  • toddkuen
  • · Replies 2 ·
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2

Undergrad Linear algebra glossary

  • Greg Bernhardt
  • · Replies 4 ·
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4

Graduate Permutations of basis elements in Clifford Algebras

  • mnb96
  • · Replies 4 ·
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4

Undergrad Calculating powers of matrices

  • rdajunior95
  • · Replies 8 ·
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8

Undergrad Can you arrange numbers 1 to 2010 to form a prime?

  • sachinism
  • · Replies 11 ·
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11

Graduate "Does Finite Group Contain Subgroup of Index 2 if Element has Order 2?

  • ForMyThunder
  • · Replies 3 ·
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3

Graduate Quaternions and associated manifolds

  • mnb96
  • · Replies 10 ·
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10

Undergrad Understanding Matrix Ranks and Null Space: A Comprehensive Guide

  • rdajunior95
  • · Replies 4 ·
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4

Undergrad Linearizing Equations: Finding Square Root of x from Plotted Data

  • Reedles
  • · Replies 1 ·
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1

Graduate Meaning of colon in group theory, if not subgroup index?

  • AgentBased
  • · Replies 2 ·
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2

Undergrad Is there a way to differentiate between numbers

  • epsi00
  • · Replies 6 ·
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6