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 A trick to calculate Pi(a) for any a?

  • eljose
  • · Replies 9 ·
Replies
9

Graduate Summing Powers of 10: Bernoulli's Method

  • damoclark
  • · Replies 6 ·
Replies
6

Undergrad How is multiplication defined and how does it relate to the natural numbers?

  • C0nfused
  • · Replies 7 ·
Replies
7

Graduate Find Idempotent Element in Z/mnZ (m,n Relatively Prime)

  • mansi
  • · Replies 2 ·
Replies
2

Graduate Proving (1+a2)(1+a3)...(1+an)=0 in a finite field

  • mansi
  • · Replies 5 ·
Replies
5

Undergrad What are the orders of groups and cyclic groups?

  • rayveldkamp
  • · Replies 2 ·
Replies
2

Graduate What is the Integral Representation of Pi(x)?

  • eljose
  • · Replies 30 ·
2
Replies
30

Graduate Is There a Solution for x^4 ≡ 2 (mod p) When p ≡ 1 (mod 4)?

  • b0mb0nika
  • · Replies 2 ·
Replies
2

Graduate Proving Isomorphism of Groups with Elements of Same Order

  • SquareCircle
  • · Replies 6 ·
Replies
6

Graduate Can the multiplicative group of a finite field be proven to be cyclic?

  • dogma
  • · Replies 2 ·
Replies
2

Graduate Proving 1 p-Sylow Subgroup of G is Normal

  • dogma
  • · Replies 2 ·
Replies
2

Undergrad Solve a Riddle with Base System Minus 1 - Nadine

  • nados29
  • · Replies 3 ·
Replies
3

Undergrad What knowledge is needed to study Wiles' proof of Fermat's Last Theorem?

  • C0nfused
  • · Replies 13 ·
Replies
13

Undergrad What does "defined up to scale" mean in homogeneous coordinates?

  • gnome
  • · Replies 2 ·
Replies
2

High School Factoring Pattern for ax^2 + bx + c

  • IndigoSwing4
  • · Replies 5 ·
Replies
5

Undergrad Farmer buying 100 animals for $4000: calves, lambs, piglets

  • lokisapocalypse
  • · Replies 2 ·
Replies
2

Undergrad Sharipov's linear algebra textbook

  • Perion
  • · Replies 25 ·
Replies
25

Undergrad What Are the Real-World Applications of Linear Transformations?

  • EvLer
  • · Replies 3 ·
Replies
3

Graduate A group theoretic puzzle in solid geometry

  • mathwonk
  • · Replies 7 ·
Replies
7

Graduate What is Rational Canonical Form and How is it Used in Rings and Fields?

  • Palindrom
  • · Replies 4 ·
Replies
4

High School What is an exact definition of numbers and cardinals?

  • C0nfused
  • · Replies 15 ·
Replies
15

Undergrad Can x^n-a=0 have n real roots for n>2?

  • msmith12
  • · Replies 3 ·
Replies
3

Graduate How can A-orthogonal vector sets be determined using positive definite matrices?

  • eckiller
  • · Replies 4 ·
Replies
4

Undergrad Examples of non-differentiable and pathological complex functions

  • nocheesie
  • · Replies 9 ·
Replies
9

Undergrad Matrix rep. of Linear Transformation

  • eckiller
  • · Replies 2 ·
Replies
2

Undergrad How to prove R² is a vector space and find its zero vector

  • matrix_204
  • · Replies 8 ·
Replies
8

Graduate A diophantine puzzle for students

  • mathwonk
  • · Replies 10 ·
Replies
10

Graduate Can any real number be represented by a continued fraction?

  • eljose
  • · Replies 24 ·
Replies
24

Undergrad Minimal and characteristic polynomial

  • cateater2000
  • · Replies 4 ·
Replies
4

Graduate Headache about Kollatz algorythm

  • FromRussiaWithLove
  • · Replies 2 ·
Replies
2

Graduate Proofing Catalan Numbers: A Combinatoric Approach

  • msmith12
  • · Replies 3 ·
Replies
3

Graduate Proving Group Properties of \left< U_n, \cdot \right>

  • hedlund
  • · Replies 8 ·
Replies
8

Undergrad Is the System of Equations Inconsistent Despite a Solved Example?

  • SomeRandomGuy
  • · Replies 7 ·
Replies
7

Undergrad Is Order of Operations the Same in Vector Spaces as in Junior High School?

  • C0nfused
  • · Replies 2 ·
Replies
2

Graduate Counting Non-Isomorphic Binary Operations on G with p Elements

  • Zaare
  • · Replies 5 ·
Replies
5

Graduate Theorem about symmetric matrices?

  • PBRMEASAP
  • · Replies 7 ·
Replies
7

Graduate When does x² + x + 1 have a root in F_p?

  • T-O7
  • · Replies 7 ·
Replies
7

Graduate Is Linear Independence Over Z the Same as Linear Independence Over R?

  • T-O7
  • · Replies 24 ·
Replies
24

Graduate Integral representation for the prime counting function

  • eljose
  • · Replies 21 ·
Replies
21

Graduate Proving the Order of Elements in a Finite Group G

  • PhysKid24
  • · Replies 5 ·
Replies
5

Graduate Solution to Frobenius Problem for N=2: Proof?

  • adamg
  • · Replies 3 ·
Replies
3

Graduate Prove that T^2 = T0 IFF R(T) C N(T)

  • eckiller
  • · Replies 2 ·
Replies
2

Undergrad Lin. transf. and linear independence

  • eckiller
  • · Replies 2 ·
Replies
2

Undergrad Proof of Equality for X1, X2, X3 Vector-Space Spans

  • EvLer
  • · Replies 5 ·
Replies
5

Graduate Sum of sin(nx)/n from 1 to infinity

  • Bossieman
  • · Replies 4 ·
Replies
4

Undergrad Proving Algebraic Nature of Root 3 + Root 2

  • lokisapocalypse
  • · Replies 2 ·
Replies
2

Undergrad What is the significance of Rn and Rm in Calculus?

  • amb123
  • · Replies 4 ·
Replies
4

Undergrad Linear independence of exponential functions and their derivatives

  • bor0000
  • · Replies 10 ·
Replies
10

Graduate Proving the Intermediate Value Theorem in Higher Dimensions using Homeomorphisms

  • mansi
  • · Replies 10 ·
Replies
10

Undergrad Finding Elements in Row Space of a Matrix: Solving for Belonging and Dependency

  • EvLer
  • · Replies 3 ·
Replies
3

Graduate Derivative Mapping in V: Understanding Rank, Nullity, Nullspace, and Range of D

  • eckiller
  • · Replies 2 ·
Replies
2

Graduate If C and D are full subcategories of each other, are they equal or equivalent?

  • phoenixthoth
  • · Replies 3 ·
Replies
3

Undergrad Merseinne Primes: Question from a Maths Dunce

  • Canute
  • · Replies 8 ·
Replies
8

Graduate Maximum Number of Terms in a Homogeneous Polynomial of m Variables and Degree n

  • danoonez
  • · Replies 3 ·
Replies
3

How many times the real amount if you paid $1 for a free bag?

  • einstein_from_oz
  • · Replies 15 ·
Replies
15

Undergrad How do you determine the coefficients for a linear transformation matrix?

  • Felix83
  • · Replies 5 ·
Replies
5

Graduate Proving E = F(u) when [E:F] = 2 and char(E) > 2

  • Palindrom
  • · Replies 19 ·
Replies
19

Graduate What Is a Basis for Vector Spaces of Finite Nonzero Term Sequences?

  • eckiller
  • · Replies 2 ·
Replies
2

Undergrad Do different eigenvector algorithms yield different results?

  • disillusioned
  • · Replies 3 ·
Replies
3

Undergrad Solving Gaussian Elimination Algorithm Problem (Matrices)

  • adc85
  • · Replies 2 ·
Replies
2

Graduate What is Hilbert space?

  • bhanukiran
  • · Replies 5 ·
Replies
5

Undergrad Testing linear independence of three column vectors

  • EvLer
  • · Replies 4 ·
Replies
4

High School Introductory Number Theory Books for High School Seniors

  • Malex
  • · Replies 12 ·
Replies
12

Undergrad What Are the Real Meanings and Purposes of Eigenvalues and Eigenvectors?

  • shankar
  • · Replies 7 ·
Replies
7

Undergrad This shows that the parallelogram law holds for complex numbers.

  • Kahsi
  • · Replies 3 ·
Replies
3

Undergrad Row reduced matrix has coefficents

  • 3.14159265358979
  • · Replies 2 ·
Replies
2

Graduate How Can I Interpolate Rotation Matrices for Skeletal Animation?

  • Dissident Dan
  • · Replies 2 ·
Replies
2

Graduate Representing a permutation, and a curiosity

  • dodo
  • · Replies 4 ·
Replies
4

Undergrad Is a solution set for a system always a vector space?

  • EvLer
  • · Replies 2 ·
Replies
2

Undergrad Is Scalar Multiplication of Vectors Written Without Parentheses?

  • C0nfused
  • · Replies 3 ·
Replies
3

Graduate Infinetely many primes of the form 3n+1

  • b0mb0nika
  • · Replies 4 ·
Replies
4

Graduate How Do You Decompose a Random n-Cycle into 2-Cycles?

  • frb
  • · Replies 1 ·
Replies
1

Undergrad Solving Vector Equation: (2i - 3j + 4k) X A = (4i +3j - k)

  • skiboka33
  • · Replies 9 ·
Replies
9

Undergrad What is the purpose of linear algebra in real life?

  • Moonbear
  • · Replies 20 ·
Replies
20

Undergrad Solving a system of linear equations with complex coefficients

  • 3.14159265358979
  • · Replies 8 ·
Replies
8

Undergrad Diagonalize a Matrix A - Normalize eigenvectors

  • DaVinci
  • · Replies 6 ·
Replies
6

Graduate How to Start Learning Lie Groups with Minimal Physics Background?

  • adityatatu
  • · Replies 2 ·
Replies
2

Graduate What is the Relationship Between the Image and Kernel of T and T^n?

  • Chen
  • · Replies 3 ·
Replies
3

Undergrad Understanding Linear Independence: Proving Non-Zero Status of One-Element Sets

  • EvLer
  • · Replies 4 ·
Replies
4

High School Why does commutivity of real numbers exist for multiplication

  • roger
  • · Replies 3 ·
Replies
3

Graduate Anoter question on vector spaces an rationnal numbers

  • seratend
  • · Replies 39 ·
2
Replies
39

Undergrad Finding Solutions to Complex Linear Systems

  • 3.14159265358979
  • · Replies 3 ·
Replies
3

High School How do u show that a matrix is diagonizable?

  • himurakenshin
  • · Replies 3 ·
Replies
3

Undergrad What are the properties of subspaces?

  • matrix_204
  • · Replies 9 ·
Replies
9

Proof that 1/2 +2/3 + 3/4 does not equal a whole number

  • Astronamus
  • · Replies 22 ·
Replies
22

Undergrad Coordinates of vector to the base

  • twoflower
  • · Replies 2 ·
Replies
2

Graduate Is the Collatz Problem Undecidable or Not?

  • MathematicalPhysicist
  • · Replies 14 ·
Replies
14

Undergrad Finding Perfect Squares Modulo a Number: 4 (mod 10) Example

  • daster
  • · Replies 9 ·
Replies
9

Undergrad Solving Linear Dynamical Systems with Eigenvectors and Eigenvalues

  • himurakenshin
  • · Replies 15 ·
Replies
15

Graduate Finding Eigenvalues of an Arbitrary Matrix

  • himurakenshin
  • · Replies 6 ·
Replies
6

Undergrad Solve system of linear congruences modulo 251, 401, 907

  • MathExpert
  • · Replies 2 ·
Replies
2

Graduate Does every subfield of ℂ contain all rational numbers?

  • poolwin2001
  • · Replies 11 ·
Replies
11

Undergrad How to prove the determinant equals the product of eigenvalues

  • Niels
  • · Replies 7 ·
Replies
7

Undergrad Is V \ U a subspace of V?

  • twoflower
  • · Replies 4 ·
Replies
4

Graduate Generalized Pell Equation and Primes

  • ramsey2879
  • · Replies 6 ·
Replies
6

Undergrad Solving Polynomials (mod p) Problems

  • ascheras
  • · Replies 3 ·
Replies
3

Graduate 3D number scattering with square and rectangular grids

  • EG
  • · Replies 22 ·
Replies
22

Graduate Parallelogram Equality+Inner Product Spaces

  • gravenewworld
  • · Replies 2 ·
Replies
2

Undergrad Which linear algebra textbook is best for a high school senior on a budget?

  • daster
  • · Replies 9 ·
Replies
9

Undergrad How to Solve the Equation X^2 + 1 = 0 (mod 5^3)?

  • brute26
  • · Replies 2 ·
Replies
2