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 What Are the Left Cosets of H in S_3?
- BustedBreaks
- · Replies 3 ·
Graduate Why does x^2≡-2 (mod p) imply a^2+2b^2=p or 2p?
- kingwinner
- · Replies 7 ·
Undergrad Proving Congruences of Primes: Show 2^((p-1)/2) = +1 (mod p)
- johndoe3344
- · Replies 2 ·
Graduate Is n Prime if Zero Products and Unique Solutions Exist in Modulo n Arithmetic?
- guyfromnola
- · Replies 1 ·
Graduate Proving (p-1)(p-2)...(p-r) ≡ (-1)^r·r! (mod p)
- tarheelborn
- · Replies 3 ·
Graduate Levi-Civita symbol and Kronecker delta
- typhoonss821
- · Replies 3 ·
Graduate Galois Extension: Proving L is Galois Over K
- math_grl
- · Replies 1 ·
Graduate Spectral theorem for self-adjoint linear transformations
- rainwyz0706
- · Replies 1 ·
Graduate Explicit and Implicit Matrix Notation Question
- Alex86
- · Replies 1 ·
Graduate How to calculate a zero of the Reimann zeta function?
- tele player
- · Replies 5 ·
Graduate Are There Exceptions to the Goldbach Conjecture for Even Numbers of the Form 2p?
- mathman
- · Replies 3 ·
Undergrad When Should Physics Students Use Eigenvectors?
- imaloonru
- · Replies 3 ·
Graduate Does g'Bg Compare with g'g When B is a Positive Definite Matrix?
- Karthiksrao
- · Replies 6 ·
Graduate Complete residue system Question
- sty2004
- · Replies 1 ·
Graduate What is the Formula for Entries in an Nxn Hilbert Matrix?
- sponsoredwalk
- · Replies 1 ·
Graduate Totient Function and phi(n)=phi(2n) for odd n
- timo1023
- · Replies 13 ·
High School Question regarding vector (cross) product
- mess1n
- · Replies 10 ·
Graduate How can Euler's totient function be proved without using prime factorizations?
- Muzza
- · Replies 2 ·
Undergrad Proving/Disproving: U and V Intersection in Rn
- jkm89
- · Replies 2 ·
Graduate Why is the count of integers coprime to m equal to kφ(m)?
- kingwinner
- · Replies 3 ·
Undergrad Can a Matrix Have Multiple Eigenbases?
- Niles
- · Replies 2 ·
Graduate Galois group isomorphic to quaternions implies degree at least 8?
- math_grl
- · Replies 6 ·
Graduate Did Paul Cohen settle the Continuum Hypothesis?
- SW VandeCarr
- · Replies 8 ·
Undergrad F(x)≡0 (mod 15) Find all roots mod 15
- kingwinner
- · Replies 25 ·
Graduate Understanding Prime Power Proofs
- mlsbbe
- · Replies 1 ·
Graduate Hadamard Product for Riemann's Xi Function
- Charles49
- · Replies 3 ·
High School [Remember Your Squares] Something I Found
- SomeGuy121
- · Replies 2 ·
Graduate Unitary Matrix Property: |Uij|2 = UijU*ji
- Niles
- · Replies 6 ·
Graduate About this strategy to prove Riemann Hypothesis
- zetafunction
- · Replies 5 ·
Graduate Are Distinct Left Cosets and Right Cosets in a Group Related?
- ivyhawk
- · Replies 3 ·
Graduate Is the Proof in Dummit and Foote's Chinese Remainder Theorem Inductive?
- icantadd
- · Replies 1 ·
Undergrad Generating Pythagorean triples from odd natural numbers
- Char. Limit
- · Replies 15 ·
Undergrad Every natural number is sum of powers of 2
- kingwinner
- · Replies 18 ·
Undergrad Are Linear Transformations of Linearly Dependent Sets Also Linearly Dependent?
- Mola
- · Replies 4 ·
Graduate Solving the Lie Bracket Question in Quantum Mechanics
- Marin
- · Replies 2 ·
Best Calculator for Matrix/Linear Algebra?
- Hacky
- · Replies 19 ·
Undergrad Dot product as matrix products?
- tgt
- · Replies 7 ·
Undergrad Non-square matrix and linear independence
- torquerotates
- · Replies 2 ·
Undergrad Why is Cramer's rule for determinants not 'symmetric'?
- Jinius
- · Replies 3 ·
Undergrad How to understand it inituitively?
- eraserxp
- · Replies 6 ·
Undergrad How to prove that (-1)u = -u in a vector space
- sbo
- · Replies 10 ·
Graduate How Do Eigen Vectors and Eigen Values Change with Dimensionality?
- esash28
- · Replies 6 ·
Undergrad Gauss seidel method of convergence
- lavster
- · Replies 2 ·
Graduate Is there a name for this construction?
- DeadWolfe
- · Replies 1 ·
Graduate Questioning the Invertibility of a Linear Operator T
- typhoonss821
- · Replies 4 ·
Graduate Trivial zeros of the Riemann zeta function
- mrbohn1
- · Replies 3 ·
Graduate Understanding Bounded Operators in Quantum Mechanics
- tommy01
- · Replies 3 ·
Undergrad Understanding Subspace Basis and Counterexample
- Caspian
- · Replies 4 ·
Graduate Is There Always a Positive Solution for the Linear Diophantine Equation ax+by=c?
- StellaLuna
- · Replies 1 ·
Undergrad Finding the angle of unit vectors
- rbnphlp
- · Replies 6 ·
Undergrad What's the use of interchanging two rows when solving a matrix?
- Juwane
- · Replies 6 ·
Graduate Prove that √(p/q) is irrational for distinct primes p and q
- olcyr
- · Replies 5 ·
High School Why do roots of integers always show 8 decimal places?
- trini
- · Replies 5 ·
Graduate What is the Operator Method for Deriving the Euler-Maclaurin Formula?
- DarkNess_wtc
- · Replies 14 ·
Graduate Alternating group is the unique subgroup of index 2 in Sn?
- ToffeeC
- · Replies 1 ·
Undergrad Subfield of the field of complex numbers
- cocobaby
- · Replies 2 ·
Undergrad Choose the signs of vectors as to maximize modulus of their sum.
- sodemus
- · Replies 2 ·
High School Prove two vectors are perpendicular (2-D)
- rbnphlp
- · Replies 4 ·
Undergrad How to tell if something has a common factor
- rsala004
- · Replies 4 ·
Graduate Proving the Rank Equivalence of Adjoint Operators
- typhoonss821
- · Replies 1 ·
Graduate Elementary property of maximal compact subgroup
- quasar987
- · Replies 1 ·
Graduate Understanding Double Inner Product Calculation in Multivariable Calculus
- Smed
- · Replies 2 ·
Graduate Why Does the Tensor Product Become a Wedge Product in Dolbeault Cohomology?
- nrobins
- · Replies 2 ·
Graduate Is Every Rank n-1 Matrix in Mn(F) Similar to a Specific Elementary Matrix?
- xixi
- · Replies 2 ·
Undergrad Do Linear Diophantine Equations Always Have a Solution?
- mlsbbe
- · Replies 1 ·
Undergrad Adjoint Operator: Proving Unique Adjoint Transformation
- typhoonss821
- · Replies 3 ·
Graduate Can Goldbach and Polignac's Conjecture be Proven with a Sieve Method?
- Andy Lee
- · Replies 20 ·
Undergrad Use an augmented matrix to prove
- John O' Meara
- · Replies 3 ·
Graduate Representation of finite group question
- quasar987
- · Replies 8 ·
Graduate Challenges in Proving Zeros of Zeta Function: Lack of Tools or Creativity?
- jacksonwalter
- · Replies 6 ·
Undergrad Prove sum of two subspaces is R^3
- tjkubo
- · Replies 6 ·
Undergrad GCD in PROOF - Solving the Puzzle
- CalleighMay
- · Replies 3 ·
Undergrad Additive Identity in Linear Algebra: V + 0 = V
- tc_11
- · Replies 3 ·
Graduate Ax≡ay (mod m) iff x≡y (mod m/(a,m))
- kingwinner
- · Replies 5 ·
Graduate Pythagorean Primes and Gaussian Primes, divisibility question
- joeblow
- · Replies 3 ·
Undergrad Proof of Common Divisor of Relatively Prime Integers
- scottstapp
- · Replies 6 ·
Undergrad 2x2 matrix A has only one eigenvalue λ with eigenvector v
- nlews
- · Replies 2 ·
Graduate Number theory and theoretical physics
- narniaoff
- · Replies 3 ·
Undergrad How to 'undo' mod, or solve equation with a mod.?
- rsala004
- · Replies 7 ·
Undergrad How to Prove Rank(A) Equals Rank(ATA)?
- katyyara
- · Replies 1 ·
Graduate Linear Independence of Vectors over C
- sir_manning
- · Replies 1 ·
Graduate Matrix Decomposition: Solving for B and D in A = B*inv(B+D)?
- TimSal
- · Replies 7 ·
Undergrad Is There an Equation for Finding All Prime Numbers?
- andrewey
- · Replies 11 ·
Graduate How to genarelize the vector product in three dimensions to higher dimensions?
- wdlang
- · Replies 2 ·
Undergrad Forward substitution in this case? Is it as simple as I think it is?
- bzz77
- · Replies 1 ·
Graduate Proving Abelian Property of Groups Using the Hypothesis ab=ca
- nataliemarie
- · Replies 4 ·
Undergrad What Are the Best Books for Studying Linear Algebra?
- bobydbcn
- · Replies 16 ·
Graduate Proving the Uniqueness of Base Representation for Integers
- sty2004
- · Replies 1 ·
Undergrad Do all functions define scalar fields?
- LucasGB
- · Replies 11 ·
Undergrad Shortcut to find if a matrix (nxn) is singular or not?
- dlevanchuk
- · Replies 4 ·
Graduate Are Coupled Linear Equations Always Solvable Analytically?
- KFC
- · Replies 3 ·
Undergrad Is trace equal to rank for idempotent matrices?
- maverick280857
- · Replies 2 ·
Undergrad Why does cyclic row permutation preserve the determinant?
- Weather Freak
- · Replies 3 ·
Undergrad What to revise for Linear Algebra?
- c-ray
- · Replies 2 ·
Undergrad What the hell are vector components?
- LucasGB
- · Replies 19 ·
Graduate What Does the Equation from the Anti-Aliasing Section in GPU Gems 2 Represent?
- rebeka
- · Replies 3 ·
Undergrad Prove (A∪B)-C ⊆ A∪(B-C)
- Ja6464
- · Replies 2 ·
Graduate Primes in set of rational numbers
- math_grl
- · Replies 8 ·
Graduate Principle of Induction and Principle of Well-Ordering
- ninjagod123
- · Replies 1 ·
Graduate Pattern in partition counting sequence with equal min, max, count and sum
- ktoz
- · Replies 1 ·