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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.

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Graduate What are the prerequisites for understanding surgery obstruction groups?

Mar 27, 2005 · Replies 9 · Apr 4, 2005

Replies: 9

Views: 3K

Undergrad [sin(t) , cos(t), e^t] are these linearly dependent?

Apr 4, 2005 · Replies 14 · Apr 4, 2005

Replies: 14

Views: 17K

Graduate Are Generalized Pell Numbers Already Known and What are Their Properties?

Mar 27, 2005 · Replies 2 · Apr 4, 2005

Replies: 2

Views: 4K

Undergrad Natural Group Homomorphism in Action

Apr 2, 2005 · Replies 3 · Apr 4, 2005

Replies: 3

Views: 3K

Undergrad Can We Conclude a=b from a.b=a.c?

Apr 1, 2005 · Replies 11 · Apr 4, 2005

Replies: 11

Views: 2K

Graduate What are the Matrices of the Regular Representation for the Cyclic Group C2?

Mar 27, 2005 · Replies 2 · Apr 4, 2005

Replies: 2

Views: 4K

Undergrad Eigenvectors and using them in matrix algebra.

Mar 27, 2005 · Replies 2 · Apr 3, 2005

Replies: 2

Views: 3K

Undergrad What are isomorphisms and how do they relate to vector spaces in linear algebra?

Mar 27, 2005 · Replies 2 · Apr 3, 2005

Replies: 2

Views: 2K

Undergrad Uncovering the Linear Relationships in Production & Sales of Yearbooks

Apr 1, 2005 · Replies 2 · Apr 2, 2005

Replies: 2

Views: 2K

Undergrad How is the Definition of Angle in Linear Algebra Derived?

Apr 1, 2005 · Replies 9 · Apr 2, 2005

Replies: 9

Views: 3K

Graduate Proof: Group G of Order 2n Has Elements of Order 2

Mar 26, 2005 · Replies 2 · Apr 2, 2005

Replies: 2

Views: 2K

Graduate Proving F-Isomorphism Between E and K

Mar 30, 2005 · Replies 16 · Apr 1, 2005

Replies: 16

Views: 3K

Graduate Hi, does anyone know the character table for the inversion group?

Mar 31, 2005 · Replies 2 · Apr 1, 2005

Replies: 2

Views: 2K

High School Perpendicular Lines in Three Space

Mar 31, 2005 · Replies 4 · Mar 31, 2005

Replies: 4

Views: 9K

Graduate Proving Solutions for x^2 ≡ -23 (mod 4*59) with Jacobi Symbol

Mar 27, 2005 · Replies 6 · Mar 31, 2005

Replies: 6

Views: 3K

Undergrad What Is the Difference Between a Subgraph and an Induced Subgraph?

Mar 29, 2005 · Replies 5 · Mar 30, 2005

Replies: 5

Views: 4K

Undergrad Handling Singular matrices in Algorithms

Mar 28, 2005 · Replies 4 · Mar 30, 2005

Replies: 4

Views: 4K

Graduate Finding the Nth Term in a Series with Different Factors

Mar 26, 2005 · Replies 4 · Mar 30, 2005

Replies: 4

Views: 4K

Graduate A certain finite group is of order 10

Mar 28, 2005 · Replies 3 · Mar 29, 2005

Replies: 3

Views: 3K

Undergrad For what values of paramater form a spanning set for P3

Mar 24, 2005 · Replies 8 · Mar 29, 2005

Replies: 8

Views: 4K

Undergrad Does Multiplying Scalars and Vectors Always Yield Zero?

Mar 28, 2005 · Replies 2 · Mar 28, 2005

Replies: 2

Views: 4K

High School Is the 2-Dimensional Cross Product Equivalent to a 90-Degree Rotation?

Mar 28, 2005 · Replies 13 · Mar 28, 2005

Replies: 13

Views: 153K

Graduate Understanding the Degree of Singularity in Matrix Operations

Mar 27, 2005 · Replies 11 · Mar 28, 2005

Replies: 11

Views: 6K

Graduate What Are the Embeddings of K in C?

Mar 28, 2005 · Replies 2 · Mar 28, 2005

Replies: 2

Views: 2K

Graduate Math Help for Finite Cyclic Group & Subgroups

Mar 27, 2005 · Replies 4 · Mar 28, 2005

Replies: 4

Views: 2K

Graduate Calculating values of the zeta function

Mar 27, 2005 · Replies 2 · Mar 27, 2005

Replies: 2

Views: 11K

Graduate Proof of Binary Quadratic Forms and Modulo Squares with Hint

Mar 25, 2005 · Replies 11 · Mar 27, 2005

Replies: 11

Views: 4K

Graduate Order of Group Elements in Abelian and Non-Abelian Groups

Mar 26, 2005 · Replies 7 · Mar 27, 2005

Replies: 7

Views: 3K

Graduate Understanding Quadric Surfaces in Computer Vision | Forsyth & Ponce

Mar 26, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 3K

Undergrad Finding A^3: Multiplication of Matrices

Mar 26, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 2K

Graduate Is It Possible to Prove Normality of Polynomials?

Mar 25, 2005 · Replies 5 · Mar 26, 2005

Replies: 5

Views: 3K

Graduate What is the construction method for creating complex numbers of any dimension?

Mar 26, 2005 · Replies 12 · Mar 26, 2005

Replies: 12

Views: 3K

Graduate Proving G is Abelian: A Group Theory Case

Mar 26, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 2K

Graduate Solving the Group Theory Conundrum: Proving 'a' is in Z(G)".

Mar 26, 2005 · Replies 3 · Mar 26, 2005

Replies: 3

Views: 3K

Undergrad Vector, Sub, Column, and Row Spaces

Mar 24, 2005 · Replies 26 · Mar 25, 2005

Replies: 26

Views: 6K

Graduate Plan of attack for showing irreducibility?

Mar 24, 2005 · Replies 6 · Mar 24, 2005

Replies: 6

Views: 4K

Undergrad Standard Basis Math: Find Point X w/ B-Coord Vector X

Mar 17, 2005 · Replies 2 · Mar 24, 2005

Replies: 2

Views: 3K

Graduate Irrational digits countably infinite?

Mar 18, 2005 · Replies 6 · Mar 24, 2005

Replies: 6

Views: 5K

Graduate Finding Conjugacy Classes in D5 Group

Mar 3, 2005 · Replies 10 · Mar 23, 2005

Replies: 10

Views: 4K

Graduate Is There a Generalization of Fermat's Last Theorem?

Mar 11, 2005 · Replies 11 · Mar 22, 2005

Replies: 11

Views: 4K

Undergrad What is the closest we have come to

Mar 21, 2005 · Replies 9 · Mar 22, 2005

Replies: 9

Views: 3K

Graduate A Simple Explanation of Zeta Function Analytic Continuation and Its Results

Mar 10, 2005 · Replies 5 · Mar 21, 2005

Replies: 5

Views: 3K

Graduate Proof Problem: Show f(x-1)=f(x) for All x ∈ E

Mar 20, 2005 · Replies 4 · Mar 21, 2005

Replies: 4

Views: 2K

Infinity: Square of Infinity + 2 Infinity

Feb 12, 2005 · Replies 24 · Mar 21, 2005

Replies: 24

Views: 9K

Graduate Is the Rank of Matrix A Equal to the Rank of Matrix M?

Mar 20, 2005 · Replies 4 · Mar 21, 2005

Replies: 4

Views: 2K

Undergrad Eigenvalues Redux: Deriving the Product of Eigenvalues = Determinant

Mar 18, 2005 · Replies 29 · Mar 20, 2005

Replies: 29

Views: 6K

Undergrad Does matrix A belong to span(A_1,A_2, )

Mar 17, 2005 · Replies 3 · Mar 18, 2005

Replies: 3

Views: 12K

Undergrad Approximating Pi and e with Linear Algebra

Mar 16, 2005 · Replies 3 · Mar 18, 2005

Replies: 3

Views: 3K

Undergrad How to Find the Inverse of a Matrix Modulo 26?

Mar 14, 2005 · Replies 24 · Mar 18, 2005

Replies: 24

Views: 22K

Graduate Question about finding last digits of numbers

Mar 10, 2005 · Replies 2 · Mar 18, 2005

Replies: 2

Views: 8K

Graduate Is x^6-2x^3-1 Irreducible Over Q?

Mar 16, 2005 · Replies 4 · Mar 17, 2005

Replies: 4

Views: 4K

Graduate Proof of composite linear transformations

Mar 9, 2005 · Replies 2 · Mar 16, 2005

Replies: 2

Views: 4K

Graduate Understanding Partially Ordered Sets: General and Specific Elements Explained

Mar 11, 2005 · Replies 11 · Mar 16, 2005

Replies: 11

Views: 4K

Graduate What Are the Eigenvalues and Characteristic Polynomials of a Special 4x4 Matrix?

Mar 15, 2005 · Replies 7 · Mar 16, 2005

Replies: 7

Views: 6K

Graduate Proving Non-Trivial Trees Have At Least 2 Vertices with Degree <2

Mar 2, 2005 · Replies 26 · Mar 15, 2005

Replies: 26

Views: 11K

Graduate Calculating Coefficients for Dirichlet Series Expansion of a Function

Mar 8, 2005 · Replies 2 · Mar 15, 2005

Replies: 2

Views: 3K

Undergrad Linear Algebra: Understanding the Concept of Proof-Based Classes

Mar 13, 2005 · Replies 4 · Mar 14, 2005

Replies: 4

Views: 6K

Graduate Need desparate help on this question concerning finding a positive integer

Mar 14, 2005 · Replies 6 · Mar 14, 2005

Replies: 6

Views: 2K

Graduate Is there a preferred orientation for the x and y axes in physics?

Mar 13, 2005 · Replies 2 · Mar 14, 2005

Replies: 2

Views: 2K

Undergrad What are Cross Products and How Do They Relate to Tensors?

Mar 13, 2005 · Replies 6 · Mar 13, 2005

Replies: 6

Views: 3K

Undergrad Solving for Integers a and b in a Divisibility Equation

Mar 13, 2005 · Replies 3 · Mar 13, 2005

Replies: 3

Views: 7K

Undergrad Questions on Remainder & Integer Divisibility

Mar 13, 2005 · Replies 4 · Mar 13, 2005

Replies: 4

Views: 3K

High School Pi doesnt have reapting random digits

Oct 14, 2004 · Replies 66 · Mar 13, 2005

3

Replies: 66

Views: 13K

Graduate Does 0 Belong to the Center of a Lie Algebra?

Mar 13, 2005 · Replies 2 · Mar 13, 2005

Replies: 2

Views: 4K

High School Is the Square Root of 2 Irrational?

Mar 5, 2005 · Replies 11 · Mar 12, 2005

Replies: 11

Views: 3K

Graduate Help me about loop invariant of LCM

Mar 5, 2005 · Replies 2 · Mar 12, 2005

Replies: 2

Views: 4K

Undergrad The GIMPS project has found a new Mersenne prime number: M42.

Feb 26, 2005 · Replies 4 · Mar 11, 2005

Replies: 4

Views: 4K

Undergrad Unraveling Euler's Formula: e^(pi*i) +1 = 0

Mar 11, 2005 · Replies 3 · Mar 11, 2005

Replies: 3

Views: 2K

Graduate Hairy billiard balls and eigenvectors

Mar 9, 2005 · Replies 4 · Mar 11, 2005

Replies: 4

Views: 4K

Graduate How to Clarify Sylow Subgroup Intersections in a Group of Order 48?

Mar 9, 2005 · Replies 7 · Mar 9, 2005

Replies: 7

Views: 4K

Graduate Determine all the ideals of the ring Z

Mar 7, 2005 · Replies 5 · Mar 8, 2005

Replies: 5

Views: 4K

Graduate Summation of S(N): Infinite/Finite?

Mar 7, 2005 · Replies 7 · Mar 8, 2005

Replies: 7

Views: 3K

Graduate Proving Continuity of F:XxI->I with Continuous Functions

Mar 7, 2005 · Replies 4 · Mar 8, 2005

Replies: 4

Views: 2K

Graduate Show 'a' is Irreducible: If R a Max Ideal in R

Mar 7, 2005 · Replies 2 · Mar 8, 2005

Replies: 2

Views: 4K

Graduate Generating Set for the Symmetric Group - Question

Mar 7, 2005 · Replies 8 · Mar 8, 2005

Replies: 8

Views: 6K

Graduate Absurdity of Cantor's Diagonal Slash

Mar 2, 2005 · Replies 44 · Mar 7, 2005

2

Replies: 44

Views: 13K

Graduate Finding the Degree of \sqrt{3} + \sqrt[3]{4} Over Q: A Polynomial Search

Mar 6, 2005 · Replies 6 · Mar 7, 2005

Replies: 6

Views: 8K

Graduate Proving Isomorphism between Vector Space and Polynomial Space

Mar 6, 2005 · Replies 2 · Mar 6, 2005

Replies: 2

Views: 3K

Undergrad Understanding Coordinate Vectors for Polynomials in P3

Mar 6, 2005 · Replies 2 · Mar 6, 2005

Replies: 2

Views: 2K

Graduate Prove/Disprove Euclidean Domains: Unique q & r Exist?

Mar 6, 2005 · Replies 2 · Mar 6, 2005

Replies: 2

Views: 3K

Undergrad Is There a Proven Method for Finding Prime Numbers?

Mar 3, 2005 · Replies 10 · Mar 6, 2005

Replies: 10

Views: 3K

Graduate Diagonalizing a 3x3 second derivative matrix

Mar 1, 2005 · Replies 7 · Mar 5, 2005

Replies: 7

Views: 7K

Undergrad How Does Euler's Formula e^(2*pi*i) Evaluate to 1?

Jan 25, 2005 · Replies 7 · Mar 5, 2005

Replies: 7

Views: 4K

Graduate Galois theory exercises

Mar 1, 2005 · Replies 7 · Mar 4, 2005

Replies: 7

Views: 6K

Undergrad How Does Fermat's Little Theorem Apply to Calculating 3^302 (mod 5)?

Mar 3, 2005 · Replies 3 · Mar 3, 2005

Replies: 3

Views: 2K

Undergrad Systems of equations - consistency

Mar 1, 2005 · Replies 5 · Mar 3, 2005

Replies: 5

Views: 10K

Undergrad Solving A^2 + 3A + I = 0: Inverse & -A-3I

Feb 28, 2005 · Replies 11 · Mar 3, 2005

Replies: 11

Views: 3K

Graduate How Can We Determine the Number of Abelian Groups of Order p^n?

Feb 23, 2005 · Replies 2 · Mar 3, 2005

Replies: 2

Views: 2K

Graduate A Question on Integrating Expansions of Infinities

Mar 1, 2005 · Replies 2 · Mar 1, 2005

Replies: 2

Views: 3K

Graduate Hypercomplex Numbers: Hamilton Postulate & Algebra

Feb 22, 2005 · Replies 2 · Mar 1, 2005

Replies: 2

Views: 3K

High School Some simple algebra that's bugging me

Feb 28, 2005 · Replies 1 · Feb 28, 2005

Replies: 1

Views: 2K

Graduate Quaternions and hypercomplex numbers are incompatible

Feb 28, 2005 · Replies 3 · Feb 28, 2005

Replies: 3

Views: 4K

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

Feb 19, 2005 · Replies 9 · Feb 28, 2005

Replies: 9

Views: 3K

Graduate Summing Powers of 10: Bernoulli's Method

Feb 27, 2005 · Replies 6 · Feb 28, 2005

Replies: 6

Views: 6K

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

Feb 27, 2005 · Replies 7 · Feb 27, 2005

Replies: 7

Views: 3K

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

Feb 27, 2005 · Replies 2 · Feb 27, 2005

Replies: 2

Views: 5K

Graduate Proving (1+a2)(1+a3)...(1+an)=0 for Any Finite Field F

Feb 26, 2005 · Replies 5 · Feb 27, 2005

Replies: 5

Views: 3K

Undergrad Group Theory Basics: Order & Cyclic Groups

Feb 19, 2005 · Replies 2 · Feb 26, 2005

Replies: 2

Views: 3K

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

Feb 23, 2005 · Replies 30 · Feb 26, 2005

2

Replies: 30

Views: 6K

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

Feb 17, 2005 · Replies 2 · Feb 25, 2005

Replies: 2

Views: 4K

Linear and Abstract Algebra

Linear and abstract algebra are branches of mathematics that deal with algebraic structures and their properties.

Linear algebra primarily focuses on vector spaces, linear transformations, and systems of linear equations. It provides essential tools for understanding geometric concepts, solving linear equations, and working with matrices. Abstract algebra, on the other hand, is a more generalized study that investigates algebraic structures such as groups, rings, and fields. It delves into the properties and relationships of algebraic systems, aiming to identify common structures and abstract patterns.

Both linear and abstract algebra are foundational areas of mathematics with applications spanning diverse fields, from physics and computer science to cryptography and optimization.

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