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 Gauss-Seidl, Gauss-Southwell, Jacobi

  • onako
  • · Replies 6 ·
Replies
6

Undergrad Why is this theorem on coplanar vectors true (LINEAR ALGEBRA)?

  • BlueRope
  • · Replies 3 ·
Replies
3

Undergrad Why does the half of the absolute value of a matrix formed with its coordinates give

  • BlueRope
  • · Replies 3 ·
Replies
3

Undergrad Confusion about linear equations

  • bentley4
  • · Replies 2 ·
Replies
2

Graduate Is the direct sum of cyclic p-groups a cyclic group?

  • lugita15
  • · Replies 6 ·
Replies
6

Graduate Finiteness of a converging random number series

  • Loren Booda
  • · Replies 3 ·
Replies
3

Proving Abelianity in Groups with $g^{2} = 1$: A Simple Proof

  • GreenGoblin
  • · Replies 6 ·
Replies
6

Find subgroups of a group for a given order

  • buckeye1973
  • · Replies 5 ·
Replies
5

Graduate Enhance Your Calculus Skills with Recommended Books for Riemann Zeta Function

  • sparsh12
  • · Replies 3 ·
Replies
3

Graduate Series of exponential prime reciprocals

  • YvesSch
  • · Replies 1 ·
Replies
1

Graduate Linear transformations as tensor.

  • The1337gamer
  • · Replies 4 ·
Replies
4

Graduate Lie group actions and submanifolds

  • mnb96
  • · Replies 7 ·
Replies
7

Graduate Casting 2x2 matrix with unit determinant in another form

  • ivl
  • · Replies 6 ·
Replies
6

Graduate Proving Cyclic Decompositions: Let T be a Linear Operator on V

  • Bhatia
  • · Replies 4 ·
Replies
4

Answer Sub Vector Spaces: U, W & V - Correct Answers

  • Yankel
  • · Replies 1 ·
Replies
1

Symmetery of a finite sequence of numbers

  • Paul Mackenzie
  • · Replies 9 ·
Replies
9

Undergrad Understanding the Product of Elementary Matrices

  • foreverdream
  • · Replies 7 ·
Replies
7

Undergrad A system of equations with more unknowns than equations

  • Liquid7800
  • · Replies 14 ·
Replies
14

Undergrad How to compute the rotation matrix

  • Renoald
  • · Replies 6 ·
Replies
6
Replies
1

High School How do you find the coordinate of a vector with the unit vector?

  • BlueRope
  • · Replies 1 ·
Replies
1

Undergrad How to Find the Smallest Integer with Specific Remainders?

  • CalculusSandwich
  • · Replies 2 ·
Replies
2

Graduate Sub-quotients and Gaussian Integer rings

  • Feryll
  • · Replies 2 ·
Replies
2

Is a Mixture of Three Chemical Solutions a Group?

  • poissonspot
  • · Replies 2 ·
Replies
2

Graduate Computing Integral Closure of Rings - Brian's Query

  • brian_m.
  • · Replies 20 ·
Replies
20

Graduate Why is SL(2,Z) the Outer-Automorphism Group of Z^2?

  • electroweak
  • · Replies 2 ·
Replies
2

Graduate The fastest algorithm for linear equations

  • Ronankeating
  • · Replies 8 ·
Replies
8

Graduate Calculating Digits of Pi in Base-16 Using the Wolfram Formula

  • Redbelly98
  • · Replies 2 ·
Replies
2

Graduate AB=I vs. BA=I: Investigating Matrix Equality in Field F

  • asmani
  • · Replies 13 ·
Replies
13

Solution to complicated systems of three variables using matrices

  • Hyunqul
  • · Replies 3 ·
Replies
3

Graduate Exploring the Riemann Hypothesis and Analytic Continuation

  • sparsh12
  • · Replies 2 ·
Replies
2

Graduate Estimating eigenvalue of perturbed matrix

  • julian
  • · Replies 7 ·
Replies
7

How to Express Vectors of a Regular Hexagon in Terms of Given Components?

  • anemone
  • · Replies 3 ·
Replies
3

Undergrad How do you count unique elements when multiplying integers from 1 to 1000?

  • epsi00
  • · Replies 18 ·
Replies
18

Graduate Test Lie Group: Show it Forms a Lie Group

  • mnb96
  • · Replies 8 ·
Replies
8

Undergrad Linear Algebra Symmetric Matrix Set Question

  • Gamble93
  • · Replies 6 ·
Replies
6

Lagrange thm: orbits as equivalence classes and cosets

  • buckeye1973
  • · Replies 4 ·
Replies
4

Graduate Splitting field of irreducible polynomial

  • joeblow
  • · Replies 4 ·
Replies
4

Graduate Elliott-Halberstam conjecture and the Riemann Hypothesis

  • flouran
  • · Replies 1 ·
Replies
1

Graduate Primality Criterion for F_n(132)

  • pedja
  • · Replies 2 ·
Replies
2

Graduate Ker A Subset Ker B: Finding a Reference

  • agnes.gorge
  • · Replies 2 ·
Replies
2

Graduate Distribution of power congruence classes

  • dec178
  • · Replies 3 ·
Replies
3

Graduate Approximation for -1 exponent expression

  • PhyPsy
  • · Replies 1 ·
Replies
1

Undergrad What is the significance of adding a constant in augmented coefficient vectors?

  • Square1
  • · Replies 2 ·
Replies
2

Undergrad Change Basis: Reasons to Write Vector in Rn Other Than Standard Basis

  • matqkks
  • · Replies 5 ·
Replies
5

Graduate Abstract Algebra: Groups and Subgroups

  • taylor81792
  • · Replies 5 ·
Replies
5

Undergrad Is Theta Commonly Used to Represent the Zero Vector in Linear Algebra?

  • TheTangent
  • · Replies 2 ·
Replies
2

Undergrad Generating full sequence with complex numbers.

  • smithnya
  • · Replies 3 ·
Replies
3

Undergrad Clear up some cross product confusion for me

  • 2slowtogofast
  • · Replies 7 ·
Replies
7

Graduate General Linear Group of a Vector Space

  • Master J
  • · Replies 11 ·
Replies
11

High School Complex Numbers - Forms and Parts

  • dotNet
  • · Replies 5 ·
Replies
5

Undergrad A few questions on abelian and normal subgroups

  • blahblah8724
  • · Replies 4 ·
Replies
4

Graduate Is Every Group of Order 15 Cyclic?

  • blahblah8724
  • · Replies 2 ·
Replies
2

Undergrad What is the mathematical topic related to finding gaps in a sequential list?

  • rtal
  • · Replies 2 ·
Replies
2

Graduate Mathematically Precise Definition of Unit

  • marschmellow
  • · Replies 2 ·
Replies
2

Undergrad How to show an isomorphism between groups?

  • blahblah8724
  • · Replies 1 ·
Replies
1

More questions on psd and pd of matrices

  • insixyears
  • · Replies 1 ·
Replies
1

Undergrad How Do CAS and Programmable Calculators Evaluate Derivatives?

  • matqkks
  • · Replies 4 ·
Replies
4

Undergrad (Algebra) Isometries on the complex plane

  • praecox
  • · Replies 3 ·
Replies
3

Graduate Algebraic Extensions, vector spaces

  • joeblow
  • · Replies 4 ·
Replies
4

Undergrad Can we still diagnolize a matrix if its eigenvectors matrix is singular?

  • AdrianZ
  • · Replies 1 ·
Replies
1

Graduate Polynomial Rings (Units and Zero divisors)

  • facepalmer
  • · Replies 4 ·
Replies
4

Graduate Abstract algebra question (math olympiad)

  • AdrianZ
  • · Replies 8 ·
Replies
8

Undergrad How to Normalize a simulated dataset to fit the actual dataset?

  • jothisadhana
  • · Replies 1 ·
Replies
1

Graduate Question about sum of primes and sample size

  • neopolitan
  • · Replies 12 ·
Replies
12

If A is nnd, then show that I + A is pd

  • insixyears
  • · Replies 3 ·
Replies
3

Graduate Question on Remark in Axler's Linear Algebra

  • Group_Complex
  • · Replies 2 ·
Replies
2

Graduate Linear Algebra Technique for Identifying Impactful Elements in a System

  • mhdella
  • · Replies 4 ·
Replies
4

Graduate Proof of commutative property in exponential matrices using power series

  • Paalfaal
  • · Replies 5 ·
Replies
5

Undergrad Why Use Matrices for Linear Transformations?

  • matqkks
  • · Replies 4 ·
Replies
4

Graduate Explicitly describing the singular locus from a finite set of polynomials

  • math2012
  • · Replies 1 ·
Replies
1

Graduate What are some other ways to solve the equation x^3+y^3+z^3+t^3=1999?

  • Mathguy15
  • · Replies 24 ·
Replies
24

Graduate Can graph spectrums be derived from incident matrices?

  • 1Truthseeker
  • · Replies 1 ·
Replies
1

Graduate Infinite-dimensional vector space question

  • Master J
  • · Replies 10 ·
Replies
10

Undergrad Modern Algebra: Permutations and Cycles

  • Phoenixtears
  • · Replies 3 ·
Replies
3

Graduate Discovering Ramsey Primes Under 1 Million

  • ramsey2879
  • · Replies 8 ·
Replies
8
Replies
4

Undergrad Question about showing that a set is a vector space

  • brinethery
  • · Replies 2 ·
Replies
2

Clearing fractions with row operations.

  • skoker
  • · Replies 2 ·
Replies
2

Graduate Basic Symmetric Group Representation Question

  • zer0skill
  • · Replies 2 ·
Replies
2

Graduate Counting function for powers of primes

  • robnybod
  • · Replies 3 ·
Replies
3

Graduate Understanding Young Diagrams from Physics 751: Solving Eqn 4.14

  • Hymne
  • · Replies 1 ·
Replies
1

Graduate Intro to Abstract Math Question about divison of integers.

  • blastoise
  • · Replies 3 ·
Replies
3

Undergrad Can the matrix be differentiated with respect to a vector

  • sainistar
  • · Replies 3 ·
Replies
3

Graduate Direct product of faithful representations into direct sum

  • rkrsnan
  • · Replies 5 ·
Replies
5

Graduate Multiple sets of linearly independent vectors

  • SvS
  • · Replies 5 ·
Replies
5

Graduate Finding Positive Integers for Irrational Number Interval

  • TJK
  • · Replies 1 ·
Replies
1

Graduate Are There Criteria for Proving Co-Primes of Vectors?

  • phynewb
  • · Replies 5 ·
Replies
5

Undergrad Finding the distance between a point and a plane using dot products

  • haackeDc
  • · Replies 3 ·
Replies
3

Graduate How many elements of order 50 are there in this group?

  • feyomi
  • · Replies 1 ·
Replies
1

Undergrad Are There Two Types of Irrational Numbers Based on Decimal Expansion Patterns?

  • lavinia
  • · Replies 7 ·
Replies
7

Undergrad Finding all primes by counting odd composite numbers

  • idiom
  • · Replies 33 ·
2
Replies
33

Find LU-Factorization of A with 1's Along Main Diagonal of L

  • skoker
  • · Replies 3 ·
Replies
3

Graduate Find rotation to align two vectors by rotation about two arbitrary axes

  • Johan_L
  • · Replies 7 ·
Replies
7

Graduate What U(n) or SU(n) or their multiplication isomorphic with SO(8)?

  • thanhsonsply
  • · Replies 5 ·
Replies
5

Undergrad What Is the Span of a List of Vectors in Linear Algebra?

  • Math Amateur
  • · Replies 7 ·
Replies
7

Undergrad Does ef|g Imply e and f Are Both Factors of g?

  • blastoise
  • · Replies 1 ·
Replies
1

Graduate Prime Ideals of direct sum of Z and Z

  • joeblow
  • · Replies 6 ·
Replies
6

High School Linear Equations (General and Standard forms: From Wikipedia)

  • jaja1990
  • · Replies 7 ·
Replies
7

Undergrad (x^k) - 1 = (x - 1)*(x^(k-1) + x^(k-2) + + x + 1)

  • General_Sax
  • · Replies 9 ·
Replies
9