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 Is A + 2A^(-1) Invertible If A Is Invertible?

  • vish_maths
  • · Replies 8 ·
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8

Undergrad Finding the Product of Primes: A Number Theory Puzzle

  • evansmiley
  • · Replies 1 ·
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1

Undergrad Show that these vectors are in a vector space?

  • ammar555
  • · Replies 6 ·
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6

Undergrad Algorithm for finding common factors of two numbers

  • Gaussianheart
  • · Replies 20 ·
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20

Undergrad Finding SVD of Matrix H: Summing H1 and H2's SVD Values?

  • EngWiPy
  • · Replies 2 ·
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2

Graduate Is a Commutative Group with a^2=1 Always a Group?

  • physicsjock
  • · Replies 4 ·
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4

Graduate Numbers which are not ultimately functions of integers

  • Loren Booda
  • · Replies 12 ·
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12

Undergrad Quadratic residues modulo 2 and 4

  • yeland404
  • · Replies 1 ·
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1

Graduate Laplace transform as rotation. In what space?

  • mclaudt
  • · Replies 3 ·
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3

Graduate Solve the Euler Totient Puzzle: Find k such that phi(k+n)=0 mod 79

  • Gaussianheart
  • · Replies 2 ·
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2

Undergrad Are These Linear Algebra Statements True or False?

  • ammar555
  • · Replies 5 ·
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5

Graduate Number system with an irrational base

  • BenVitale
  • · Replies 6 ·
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6

Undergrad What Is the Difference Between a Transition Matrix and a Jacobian?

  • HMT
  • · Replies 3 ·
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3

Graduate Is \( u^p \) a root of \( f(x) \) over \( GF(p) \) if \( u \) is a root?

  • joeblow
  • · Replies 3 ·
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3

Graduate Why does ⟨x_i, y_i⟩ ≠ 0 in finite reflection groups preliminaries?

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Rigorous abstract algebra book for undergraduates and graduates

  • dijkarte
  • · Replies 5 ·
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5

Graduate Can you find the maximum distance in the travelling salesman problem?

  • sparsh12
  • · Replies 2 ·
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2

Graduate Maximizing sum of products from two finite sets

  • sparsh12
  • · Replies 2 ·
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2

Graduate Representation Theory of Finite Groups - CH 18 Dummit and Foote

  • Math Amateur
  • · Replies 8 ·
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8

Graduate Is Number Line Density Constant or Variable?

  • Loren Booda
  • · Replies 9 ·
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9

Graduate Negative diagonal elements in Incomplete Cholesky Decompostion

  • Hassan2
  • · Replies 4 ·
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4

Graduate Logarithmic Integral and Primes

  • Frogeyedpeas
  • · Replies 2 ·
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2

Graduate The Orthonormality of real valued Functions

  • ReubenThorpe
  • · Replies 7 ·
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7

Graduate Are any two infinite-dim. V.Spaces isomorphic?

  • Bacle
  • · Replies 21 ·
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21

Graduate Product of two subgroups and intersection with p-subgroup

  • moont14263
  • · Replies 1 ·
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1

Undergrad Minimum number of elements in one set to sum to all in another

  • TylerH
  • · Replies 7 ·
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7

Graduate Proof of the Order Divisibility Property

  • squire636
  • · Replies 4 ·
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4

Graduate Can Dependent Variables Defy E(X)E(Y) = E(XY) in Probability?

  • georg gill
  • · Replies 4 ·
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4

Number of elements in a ring with identity.

  • AkilMAI
  • · Replies 8 ·
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8

Why does 1_R = 0_R imply the ring has only one element?

  • Stephen88
  • · Replies 20 ·
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20

Graduate A general condition on polynomial roots

  • lunogled
  • · Replies 3 ·
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3

Graduate Order of error for rational approximation of irrationals

  • Liedragged
  • · Replies 4 ·
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4

Graduate How Can You Find the Number of Conjugation Permutations in a Group?

  • physicsjock
  • · Replies 3 ·
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3

Graduate Reduced Grobner basis form a regular sequence?

  • math2012
  • · Replies 6 ·
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6

Graduate A question regarding arithmetic progressions

  • drag12
  • · Replies 1 ·
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1

Graduate Infinitely many solutions ? n*phi(n)=k

  • Gaussianheart
  • · Replies 5 ·
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5

High School Proofs and puzzles for beginning mathematicians

  • Imaginer1
  • · Replies 9 ·
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9

Graduate Primality Criteria for Wagstaff numbers

  • pedja
  • · Replies 2 ·
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2

Prove det(I + uv^T) = 1 + v^T u for u,v in R^n

  • Amer
  • · Replies 1 ·
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1

Graduate Is V a vector space? and Show that W is not a subspace

  • mosawi
  • · Replies 12 ·
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12

Graduate Would someone tell me about the importance of number theory?

  • AdrianZ
  • · Replies 8 ·
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8

Undergrad Proving A = B in Linear Algebra using (A-B)D = 0 and Inverses

  • Jet1045
  • · Replies 2 ·
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2

System Ax=b with infinite solutions: when does rank(A|b)=rank(A)?

  • Yankel
  • · Replies 1 ·
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1

Undergrad Which Book Should I Start With for Learning Number Theory?

  • Genericcoder
  • · Replies 10 ·
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10

Graduate Show that if p^e divides n then p-1 and p^(e-1) divide φ(n)

  • rechinball
  • · Replies 3 ·
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3

Proving Irreducibility of x^4 −7 Using Polynomial Theorems

  • Poirot1
  • · Replies 1 ·
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1

Undergrad Associative Property of Convolution?

  • DWill
  • · Replies 8 ·
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8

Which Coefficient Ring Makes f=x^2+1 Irreducible?

  • Poirot1
  • · Replies 4 ·
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4

Undergrad Functions similar to Collatz that end in 2, 3, or 4

  • NightFury
  • · Replies 7 ·
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7

Graduate Proving the Infinitude of Primes: Euler's Proof and Its Limitations

  • MostlyConfusd
  • · Replies 2 ·
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2

Graduate Finding the 12th vector set from 11 polygon sequences

  • italianboy
  • · Replies 3 ·
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3

Ring Theory: Proving Subrings and Ring Generation

  • Poirot1
  • · Replies 1 ·
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1

Undergrad How were these linear motion equations derived?

  • jshpark
  • · Replies 1 ·
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1

Graduate Is the concept of prime numbers biased by their factorization definitions?

  • sciencecrazy
  • · Replies 1 ·
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1
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1

Graduate Problem with minimizing the matrix norm

  • mnb96
  • · Replies 2 ·
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2

Graduate Is i^i equal to e^-(pi/2 + 2npi)?

  • Chantry
  • · Replies 6 ·
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6

Undergrad Can't understand technique for computing transformation matrix

  • coreluccio
  • · Replies 3 ·
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3

Undergrad What is the Proof of the Size of Divisors for Integers?

  • cariad69
  • · Replies 2 ·
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2

Graduate Proving that a subset of ℝ⁴ is an affine subset

  • tamintl
  • · Replies 19 ·
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19

Graduate Squared norms: difference or notational convenience

  • onako
  • · Replies 2 ·
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2

Why does every finite domain have an identity element?

  • AkilMAI
  • · Replies 1 ·
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1

Undergrad How can the endless square root problem be solved?

  • Chirag B
  • · Replies 10 ·
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10

Undergrad What is the Correct Way to Find Eigenvalues and Eigenvectors of a Matrix?

  • Seon
  • · Replies 1 ·
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1

Prove Ring with Identity on Set S with One Element x

  • Stephen88
  • · Replies 3 ·
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3

Undergrad Gram-Schmidt Method for orthogonal basis

  • foreverdream
  • · Replies 2 ·
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2

Graduate The approach to project out certain vector

  • onako
  • · Replies 2 ·
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2

Graduate Symmetry Groups Algebras Commutators Conserved Quantities

  • friend
  • · Replies 1 ·
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1

Is (a,b) the GCD of a and b in a Divisibility Proof?

  • wloger
  • · Replies 2 ·
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2

Graduate What is the canonical isomorphism ℂ ⊗_ℝ ℂ ≅ ℂ ⊕ ℂ?

  • quasar987
  • · Replies 11 ·
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11

Graduate Determine if a matrix if positive definite

  • onako
  • · Replies 5 ·
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5

Graduate Some Flat Equation Prime Number Aproximations

  • qpwimblik
  • · Replies 5 ·
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5

Graduate How Do You Calculate the Dimension of F(u,v) Over F(u)?

  • Wingeer
  • · Replies 3 ·
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3

Graduate Nilpotent operator or not given characteristic polynomial?

  • fishshoe
  • · Replies 4 ·
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4

Graduate A prime limit that seems to approach a constant

  • robnybod
  • · Replies 5 ·
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5

Graduate Can You Find the Prime Factors of m Using Euler's Totient Function?

  • squire636
  • · Replies 2 ·
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2

High School How to Add Base-Six Numbers and Express the Sum 3546 + 4326 as a Base-Six Number

  • PotentialE
  • · Replies 1 ·
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1

Graduate Linear or conjugate operators and automorphisms on the lattice of subspaces

  • Fredrik
  • · Replies 2 ·
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2

Graduate New Test for Primes form 8n =/- 3

  • ramsey2879
  • · Replies 2 ·
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2

Graduate Consecutive Numbers in the Fibbonacci Sequence and Sums of Two Squares

  • Imaginer1
  • · Replies 2 ·
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2

Graduate Do Quasiperfect Numbers Really Exist?

  • Joseph Fermat
  • · Replies 3 ·
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3

Graduate How to factor a polynomial modulo p?

  • joebohr
  • · Replies 3 ·
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3

Graduate Product of a third- and second-order tensor.

  • Nimlidor
  • · Replies 6 ·
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6

High School Easy algorithms to produce big numbers

  • Loren Booda
  • · Replies 12 ·
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12

Undergrad Linear Algebra. Proving differentiable functions are a vector space.

  • datran
  • · Replies 3 ·
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3

Graduate An error related with matrix exponential

  • umut_caglar
  • · Replies 5 ·
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5

Graduate Qube root of 2, zero of second order polynomial

  • jostpuur
  • · Replies 7 ·
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7

Graduate Why does multiplying elements of Z[α] give the conjugate of α?

  • blahblah8724
  • · Replies 1 ·
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1

Graduate Fibonacci sequence- advanced realations

  • Rocketboy123
  • · Replies 3 ·
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3

Graduate Exercise 12 from Hoffman and Kunze Linear Algebra

  • asmani
  • · Replies 3 ·
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3

Undergrad Can Extending Vectors from ℝm to ℝm+1 Alter Their Representation?

  • daiviko
  • · Replies 1 ·
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1

High School Simple Polynomial Factorization

  • naptor
  • · Replies 11 ·
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11

Solve x^6=7 in F19: 6 Solutions

  • MikeD2
  • · Replies 4 ·
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4

Graduate Some questions about solving eigenproblems to do modal analysis

  • blah900
  • · Replies 3 ·
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3

Subgroups of a Cyclic Group G of Order 12

  • GreenGoblin
  • · Replies 16 ·
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16

Which statement about eigenvalues and eigenvectors is not true?

  • Yankel
  • · Replies 9 ·
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9

Graduate What are Mirror Planes and Distinct Symmetry Transformations in Mathematics?

  • spaghetti3451
  • · Replies 1 ·
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1

Graduate Why is Te_2 determined by Te_1 in orthogonal transformations?

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Cosets and Vector Spaces Question

  • Master J
  • · Replies 9 ·
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9

Graduate Finite abelian group into sequence of subgroups

  • jav
  • · Replies 1 ·
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1