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

Undergrad Proof: A is Invertible if and only if A^T*A is Invertible | Matrix Algebra

  • physicsss
  • · Replies 5 ·
Replies
5

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

  • Don Aman
  • · Replies 3 ·
Replies
3

Undergrad Abstract Algebra book suggestions

  • Karate Chop
  • · Replies 18 ·
Replies
18

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

  • keebs
  • · Replies 9 ·
Replies
9

Graduate Congruence Problem Solution for FLT

  • vantheman
  • · Replies 19 ·
Replies
19

Graduate Help Needed: Solving Integer Equations with GCD = 1 - Angelo Spina

  • angelo
  • · Replies 4 ·
Replies
4

Graduate Does Deutsch's Algorithm Reveal Insights Into Prime Numbers?

  • Loren Booda
  • · Replies 5 ·
Replies
5

Undergrad Orthonormal, Orthogonal, Perpendicular

  • Nusc
  • · Replies 4 ·
Replies
4

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

  • quasar987
  • · Replies 67 ·
3
Replies
67

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

  • physicsss
  • · Replies 3 ·
Replies
3

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

  • SSSUNNN
  • · Replies 4 ·
Replies
4

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

  • physicsss
  • · Replies 4 ·
Replies
4

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

  • Cristi-Tota
  • · Replies 1 ·
Replies
1

High School Matrices in more than 2 dimensions

  • The Rev
  • · Replies 5 ·
Replies
5

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

  • Chen
  • · Replies 2 ·
Replies
2

Undergrad Finding the Span of u1 & u2 in R^3

  • physicsss
  • · Replies 6 ·
Replies
6

Graduate Constructing a Cartesian Closed Topos for Real Closed Fields

  • Hurkyl
  • · Replies 2 ·
Replies
2

Graduate Transpose of Matrix as Linear Map

  • chingkui
  • · Replies 2 ·
Replies
2

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

  • flop
  • · Replies 2 ·
Replies
2

Undergrad New to induction, stuck on a proof and i need some help

  • johnnyICON
  • · Replies 8 ·
Replies
8

Graduate Finding Eigenvectors for Coordinate transformation

  • pjg
  • · Replies 11 ·
Replies
11

Undergrad Vector Space Problem: Is {x1,x2,x3} a Vector Space?

  • physicsss
  • · Replies 13 ·
Replies
13

Graduate Complex roots problem (a proof by induction)

  • TomMe
  • · Replies 12 ·
Replies
12

Undergrad Linear and Abstract Algebra textbooks

  • Icebreaker
  • · Replies 48 ·
2
Replies
48

Graduate Alsings hypothesis of integers bigger than 2

  • HAP
  • · Replies 2 ·
Replies
2

Undergrad Solving 4x4 Determinant - Find a and b

  • cnky
  • · Replies 8 ·
Replies
8

Undergrad Is Sudoku Addicting and Mathematically Complex?

  • quetzalcoatl9
  • · Replies 2 ·
Replies
2

Undergrad Finding a Basis for M2's Symmetric Matrices

  • heman
  • · Replies 3 ·
Replies
3

Undergrad Simultaneous trigonometric equations

  • John O' Meara
  • · Replies 2 ·
Replies
2

High School Why is gcd important in number theory?

  • honestrosewater
  • · Replies 21 ·
Replies
21

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

  • amcavoy
  • · Replies 2 ·
Replies
2

Graduate Natural isomorphism of VxV* and End(V)

  • Don Aman
  • · Replies 22 ·
Replies
22

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

  • quasar987
  • · Replies 19 ·
Replies
19

Graduate Curious about a pattern to prime products.

  • rshriner
  • · Replies 13 ·
Replies
13

Graduate Equivalent conditions for hermitian matrix

  • twoflower
  • · Replies 5 ·
Replies
5

Graduate Asymptotic formula for Mertens function

  • keebs
  • · Replies 4 ·
Replies
4

Undergrad How to find all solutions of Pell equation

  • murshid_islam
  • · Replies 14 ·
Replies
14

Graduate Something about hermitian matrixes

  • twoflower
  • · Replies 5 ·
Replies
5

Undergrad Kernel of differentiation and integration

  • madking153
  • · Replies 5 ·
Replies
5

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

  • quasar987
  • · Replies 29 ·
Replies
29

Undergrad A simple permutation question or not so simple

  • johnnyICON
  • · Replies 9 ·
Replies
9

Graduate Question about quadratic residues

  • T.Rex
  • · Replies 5 ·
Replies
5

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

  • twoflower
  • · Replies 4 ·
Replies
4

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

  • m00c0w
  • · Replies 3 ·
Replies
3

Undergrad Nontrivial Subspace with Equal Dimensions: Linear Algebra Example

  • dan0
  • · Replies 2 ·
Replies
2

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

  • rayveldkamp
  • · Replies 2 ·
Replies
2

Graduate Splitting Polynomials Over Finite Fields: Fact or Fiction?

  • snoble
  • · Replies 13 ·
Replies
13

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

  • James Jackson
  • · Replies 2 ·
Replies
2

Graduate Something that's been frustrating me

  • Manchot
  • · Replies 4 ·
Replies
4

High School 0/0 Anything divided by zero is undefined

  • madness
  • · Replies 11 ·
Replies
11

Undergrad Complex conjugate of a 5 x 5 matrices?

  • ayalam
  • · Replies 7 ·
Replies
7

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

  • Baggio
  • · Replies 8 ·
Replies
8

Graduate Proving the Convergence of a Sequence Defined by Induction

  • johnnyICON
  • · Replies 8 ·
Replies
8

High School New to Planes, understanding them.

  • DOCMUR
  • · Replies 3 ·
Replies
3

Undergrad How Can I Determine if a Matrix is Positive?

  • Seckin Sefi
  • · Replies 2 ·
Replies
2

Graduate Defining an Inner Product on the Vector Space of Polynomials in x

  • Zurtex
  • · Replies 17 ·
Replies
17

Undergrad Theorem regarding mod properties

  • plusunim
  • · Replies 5 ·
Replies
5

Graduate Some linear algebra proofs I couldn't figure out: Help

  • hola
  • · Replies 20 ·
Replies
20

Graduate Proving Orthogonality of Non-Zero Vectors

  • mattmns
  • · Replies 13 ·
Replies
13

Undergrad Solving Linear Algebra Final Questions with Help

  • Gale
  • · Replies 26 ·
Replies
26

Graduate Let V be a 5 dimensional vector space

  • laminatedevildoll
  • · Replies 2 ·
Replies
2

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

  • Icebreaker
  • · Replies 2 ·
Replies
2

Undergrad Markov chains and steady state vectors

  • Physics is Phun
  • · Replies 3 ·
Replies
3

Graduate Proving Solutions of Linear Transformations Using Kernel and Fixed Vectors

  • laminatedevildoll
  • · Replies 4 ·
Replies
4

Undergrad Understanding Right and Left Handed Systems in Vector Calculus

  • laminatedevildoll
  • · Replies 2 ·
Replies
2

Graduate What's the probability of R in C?

  • Sabine
  • · Replies 12 ·
Replies
12

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

  • matness
  • · Replies 11 ·
Replies
11

Undergrad Proving a number is divisible by 48

  • johnnyICON
  • · Replies 33 ·
2
Replies
33

Undergrad Do Infinitely Many Prime Pairs Exist?

  • nnnnnnnn
  • · Replies 93 ·
4
Replies
93

Graduate Show Reducibility of x^4+1 Modulo p

  • Palindrom
  • · Replies 11 ·
Replies
11

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

  • The Rev
  • · Replies 83 ·
3
Replies
83

Undergrad Prove: GCD of a, b and d is Equal to GCD of a and b

  • BicycleTree
  • · Replies 11 ·
Replies
11

Graduate Vector Space Basis and the Axiom of Choice: Are They Interchangeable?

  • chingkui
  • · Replies 15 ·
Replies
15

Graduate Eigenvalues, eigenvectors question

  • jhson114
  • · Replies 4 ·
Replies
4

Graduate Solving Quantum Computation: Diagonalizing Y & Z Operators

  • James Jackson
  • · Replies 2 ·
Replies
2

Undergrad Quick questions about modular arithmetic

  • johnnyICON
  • · Replies 8 ·
Replies
8

Undergrad Linear algebra: determinants and eigenvalues

  • jhson114
  • · Replies 15 ·
Replies
15

Graduate Powers of a non-diagonalizable matrix?

  • TomMe
  • · Replies 6 ·
Replies
6

High School What is the Fibonacci Sequence and why is it so intriguing?

  • Leopold Infeld
  • · Replies 6 ·
Replies
6

Graduate Representation of Group OH: Ex, Ey & Ez

  • PhysKid24
  • · Replies 3 ·
Replies
3

Undergrad Verify Linear Transformations: 3.4a, 3.4b

  • laminatedevildoll
  • · Replies 2 ·
Replies
2

High School Understanding Congruency and Its Applications

  • johnnyICON
  • · Replies 3 ·
Replies
3

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

  • RandallB
  • · Replies 2 ·
Replies
2

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

  • quasar987
  • · Replies 14 ·
Replies
14

Undergrad How much commutativity in associativity

  • Kocur
  • · Replies 9 ·
Replies
9

Graduate What Defines Mainvectors in the Context of Eigenvalue Multiplicities?

  • yeus
  • · Replies 3 ·
Replies
3

Undergrad Is Infinity Just an Inverse Zero?

  • Coqui
  • · Replies 6 ·
Replies
6

Solving a Problem: Seeking Feedback

  • laminatedevildoll
  • · Replies 2 ·
Replies
2

High School Is Subtraction of Real Numbers Associative or Not?

  • Kocur
  • · Replies 3 ·
Replies
3

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

  • eckiller
  • · Replies 2 ·
Replies
2

Graduate Polar Coordinates: A Nicer Way to Define?

  • quasar987
  • · Replies 10 ·
Replies
10

Undergrad Little excercise about bases (question)

  • TomMe
  • · Replies 16 ·
Replies
16

Undergrad Cross product of polar coordinates

  • tiagobt
  • · Replies 2 ·
Replies
2

Undergrad Question regarding linear transformation

  • Mathman23
  • · Replies 2 ·
Replies
2

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

  • AntonVrba
  • · Replies 5 ·
Replies
5

Undergrad Proving B^2=B & Finding det(B) | Linear Algebra Exercises

  • hola
  • · Replies 7 ·
Replies
7

Undergrad The Mysteries of Number Theory: Essential Notes for Beginners

  • maverickmathematics
  • · Replies 6 ·
Replies
6

Graduate Free Algebra Notes: Linear Algebra, Group Theory, Riemann Roch

  • mathwonk
  • · Replies 17 ·
Replies
17

High School Finding Shortcuts to Solve Big Math Problems

  • slug
  • · Replies 8 ·
Replies
8

Graduate Is T an Isomorphism and How Can It Be Proven?

  • laminatedevildoll
  • · Replies 4 ·
Replies
4