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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 Can Someone explain Dedikind cuts?

Dec 14, 2004 · Replies 11 · Dec 15, 2004

Replies: 11

Views: 5K

Graduate Solving Vector Spaces Problems with Calculus

Dec 13, 2004 · Replies 3 · Dec 14, 2004

Replies: 3

Views: 3K

Graduate A Short Course on Quantum Matrices: Understanding Notation Basics

Dec 6, 2004 · Replies 2 · Dec 14, 2004

Replies: 2

Views: 4K

High School Why Does (1/3)*3 = 1 and Not .9 Repeating?

Dec 5, 2004 · Replies 53 · Dec 13, 2004

2

Replies: 53

Views: 12K

Undergrad Understanding the Pseudoinverse: What is it and How Does it Work?

Dec 11, 2004 · Replies 4 · Dec 13, 2004

Replies: 4

Views: 6K

Undergrad How Many Left Cosets of <a^4> in <a> Are There?

Dec 13, 2004 · Replies 4 · Dec 13, 2004

Replies: 4

Views: 4K

Undergrad How do I show that A is not diagonalizable?

Dec 13, 2004 · Replies 3 · Dec 13, 2004

Replies: 3

Views: 2K

Undergrad Is my linear algebra book's definition of Euclidean space correct?

Dec 9, 2004 · Replies 6 · Dec 13, 2004

Replies: 6

Views: 4K

High School How to Prove Zero Product Property for Rational Numbers?

Dec 12, 2004 · Replies 3 · Dec 12, 2004

Replies: 3

Views: 3K

Graduate Orthogonal projection, orthonormal basis, coordinate vector of the polynomial?

Dec 4, 2004 · Replies 2 · Dec 11, 2004

Replies: 2

Views: 15K

Graduate LUB and Nested Interval Equivalancy

Dec 8, 2004 · Replies 5 · Dec 11, 2004

Replies: 5

Views: 5K

Graduate How Rademacher Derived His Formula for Partitioning Integers

Mar 7, 2004 · Replies 4 · Dec 11, 2004

Replies: 4

Views: 3K

Undergrad Modulo arithmetic (?) question

Nov 30, 2004 · Replies 10 · Dec 11, 2004

Replies: 10

Views: 3K

Graduate Surjective and bijective mapping

Dec 10, 2004 · Replies 5 · Dec 10, 2004

Replies: 5

Views: 7K

Undergrad Proof of ab=0 <--> (a=0 or b=0) without Division

Dec 2, 2004 · Replies 17 · Dec 9, 2004

Replies: 17

Views: 4K

High School Efficient Methods for 3x3 Matrix Multiplication

Dec 8, 2004 · Replies 2 · Dec 8, 2004

Replies: 2

Views: 3K

Is There a Numerical Connection to the End of the 'Curse of the Bambino'?

Dec 8, 2004 · Replies 4 · Dec 8, 2004

Replies: 4

Views: 3K

Undergrad Finding the eigenvalue for a given graph

Dec 8, 2004 · Replies 2 · Dec 8, 2004

Replies: 2

Views: 2K

Graduate Vectors Property: Necessary & Sufficient Conditions

Dec 1, 2004 · Replies 2 · Dec 8, 2004

Replies: 2

Views: 2K

Graduate How Can You Prove the Axioms of Norms and Use Them to Test Convergence?

Dec 6, 2004 · Replies 5 · Dec 7, 2004

Replies: 5

Views: 2K

Graduate Prove A' is the Generalized Inverse of A When A'A is Idempotent

Dec 7, 2004 · Replies 11 · Dec 7, 2004

Replies: 11

Views: 3K

Undergrad Permutations and Transpositions problem help

Dec 5, 2004 · Replies 11 · Dec 6, 2004

Replies: 11

Views: 5K

Graduate Verifying F_5[x]/(x^4+1) is a Field

Dec 3, 2004 · Replies 12 · Dec 6, 2004

Replies: 12

Views: 3K

Graduate What is the concept of injection and surjection?

Dec 5, 2004 · Replies 5 · Dec 6, 2004

Replies: 5

Views: 3K

Graduate Total potential energy in matrix

Dec 5, 2004 · Replies 2 · Dec 6, 2004

Replies: 2

Views: 5K

Undergrad Find Linear Combinations for {1, x, x^2, x^3}

Dec 1, 2004 · Replies 2 · Dec 5, 2004

Replies: 2

Views: 2K

Undergrad Cyclic Group U(14): Generating Elements with <3> to Show Cyclic Property

Dec 2, 2004 · Replies 3 · Dec 5, 2004

Replies: 3

Views: 4K

Graduate Is x^4 - 14x^2 + 9 = 0 irreducible in Q?

Dec 3, 2004 · Replies 2 · Dec 5, 2004

Replies: 2

Views: 3K

Undergrad What is the connection between Diophantine equations and number theory?

Nov 27, 2004 · Replies 2 · Dec 4, 2004

Replies: 2

Views: 3K

Undergrad Help whit a problem. (I have no idea)

Dec 3, 2004 · Replies 3 · Dec 4, 2004

Replies: 3

Views: 2K

Graduate What are the key properties of functors and how are they used in mathematics?

Dec 1, 2004 · Replies 4 · Dec 2, 2004

Replies: 4

Views: 2K

Graduate Lie group (additional condition)

Nov 25, 2004 · Replies 2 · Dec 2, 2004

Replies: 2

Views: 2K

Graduate I need a proof for this binomial property.

Oct 6, 2004 · Replies 6 · Nov 30, 2004

Replies: 6

Views: 4K

Graduate Why are groups, rings, and fields defined in the way that they are?

Nov 29, 2004 · Replies 3 · Nov 30, 2004

Replies: 3

Views: 6K

Graduate Is H Always a Normal Subgroup in a Group of Even Order?

Nov 22, 2004 · Replies 2 · Nov 30, 2004

Replies: 2

Views: 2K

Undergrad How Can I Find All Homomorphisms from Z to Z mod 12?

Nov 22, 2004 · Replies 2 · Nov 30, 2004

Replies: 2

Views: 3K

Undergrad Theorema of Bezout: Finding f & e with Examples

Nov 21, 2004 · Replies 5 · Nov 29, 2004

Replies: 5

Views: 2K

Graduate Can De Branges' Theorem Make Factoring Prime Numbers Easier for RSA Encryption?

Nov 28, 2004 · Replies 6 · Nov 29, 2004

Replies: 6

Views: 4K

High School Multiplication (powers) of fractions

Nov 17, 2004 · Replies 19 · Nov 28, 2004

Replies: 19

Views: 37K

Graduate Does Every Linear Operator Have a Nontrivial Invariant Subspace?

Nov 11, 2004 · Replies 6 · Nov 28, 2004

Replies: 6

Views: 7K

Graduate Proving F is Finite: A Perspective on Ring Homomorphisms

Nov 18, 2004 · Replies 3 · Nov 28, 2004

Replies: 3

Views: 5K

Graduate A bit of trouble with Galois groups

Nov 19, 2004 · Replies 2 · Nov 27, 2004

Replies: 2

Views: 3K

Undergrad Finding Cosets with H = {0, 3, 6} under Z(9): Understanding the Starting Values

Nov 19, 2004 · Replies 2 · Nov 26, 2004

Replies: 2

Views: 2K

Undergrad Solving a System of Equations with Matrix

Nov 17, 2004 · Replies 2 · Nov 24, 2004

Replies: 2

Views: 3K

Undergrad Optimizing Integer Comparison without If Statements

Nov 17, 2004 · Replies 5 · Nov 24, 2004

Replies: 5

Views: 5K

Undergrad Linear Algebra HELP: Closest Vector to v in R^4

Nov 17, 2004 · Replies 2 · Nov 24, 2004

Replies: 2

Views: 2K

Graduate Is <Z,+> with <Z,+> a valid isomorphism? Why or why not?

Nov 22, 2004 · Replies 11 · Nov 23, 2004

Replies: 11

Views: 3K

Graduate Solve Matrix Hyperplane: Find A & B | Please Help!

Nov 22, 2004 · Replies 3 · Nov 23, 2004

Replies: 3

Views: 2K

Graduate Prove Beta is an isomorphism of groups

Nov 22, 2004 · Replies 3 · Nov 23, 2004

Replies: 3

Views: 3K

Undergrad Nullspace and Column Space Question

Nov 21, 2004 · Replies 2 · Nov 22, 2004

Replies: 2

Views: 9K

Graduate What is the group of automorphisms of S_3?

Nov 20, 2004 · Replies 2 · Nov 22, 2004

Replies: 2

Views: 3K

Graduate Eigenvalues Problem: Show Inverse of Diagonalizable Matrix A

Nov 21, 2004 · Replies 4 · Nov 22, 2004

Replies: 4

Views: 2K

Graduate How Does Euler's Formula Lead to e^(iπ) = -1?

Nov 21, 2004 · Replies 3 · Nov 21, 2004

Replies: 3

Views: 3K

Undergrad Can a non-zero matrix multiply itself to become zero matrix?

Nov 18, 2004 · Replies 6 · Nov 21, 2004

Replies: 6

Views: 21K

Graduate Number of Elements of Order 5 in S7 Permutation Group

Nov 14, 2004 · Replies 9 · Nov 21, 2004

Replies: 9

Views: 4K

Graduate How Do You Find Automorphism in a Group G?

Nov 18, 2004 · Replies 10 · Nov 19, 2004

Replies: 10

Views: 10K

Graduate Existence of a Polynomial Divisor for Roots in a Field Extension

Nov 17, 2004 · Replies 2 · Nov 19, 2004

Replies: 2

Views: 3K

Graduate Proving Finite Solutions of phi(x)=n for Fixed Integer n

Nov 18, 2004 · Replies 2 · Nov 18, 2004

Replies: 2

Views: 5K

Undergrad Write the system in equation form?

Nov 9, 2004 · Replies 2 · Nov 16, 2004

Replies: 2

Views: 5K

Graduate What Is the Relationship Between m, n, and x in the 3x+1 Problem?

Nov 15, 2004 · Replies 2 · Nov 16, 2004

Replies: 2

Views: 3K

Undergrad Finding the Basis for Repeated Eigenvalues: Explained

Nov 9, 2004 · Replies 2 · Nov 16, 2004

Replies: 2

Views: 8K

Undergrad Is There a Solution to the Equation A=x^b mod p?

Nov 14, 2004 · Replies 3 · Nov 15, 2004

Replies: 3

Views: 5K

Undergrad Prove Pythagorean Triples: 3k, 4k, 5k | Answer Yay/Nay

Nov 3, 2004 · Replies 7 · Nov 14, 2004

Replies: 7

Views: 6K

Undergrad What is the relationship between GCD, LCM, and relatively prime numbers?

Oct 27, 2004 · Replies 3 · Nov 13, 2004

Replies: 3

Views: 13K

Graduate RSA Encryption: Finding Primes to Make Decryption Difficult

Nov 9, 2004 · Replies 3 · Nov 13, 2004

Replies: 3

Views: 4K

High School What Is the Alphabetical Rank of Ought and Tough?

Nov 4, 2004 · Replies 2 · Nov 11, 2004

Replies: 2

Views: 4K

Graduate Why Does [d/[n]^2] * n Find the Closest Point to the Origin on a Plane?

Nov 4, 2004 · Replies 2 · Nov 11, 2004

Replies: 2

Views: 14K

Undergrad Geometric Descr. of 1-1 Function from Square to Circle

Nov 9, 2004 · Replies 2 · Nov 10, 2004

Replies: 2

Views: 2K

Graduate Column Spaces and Rank of Matrix Multiplication: Insights and Proof

Nov 3, 2004 · Replies 2 · Nov 10, 2004

Replies: 2

Views: 5K

High School Is a Progression a Series or a Sequence?

Nov 7, 2004 · Replies 3 · Nov 9, 2004

Replies: 3

Views: 3K

Graduate Group Actions on Sets: Understanding the Permutation Group S_3

Nov 6, 2004 · Replies 3 · Nov 8, 2004

Replies: 3

Views: 4K

Graduate Are Non-Prime Numbers Affected by Reimann's Critical Line?

Oct 30, 2004 · Replies 11 · Nov 7, 2004

Replies: 11

Views: 3K

Undergrad Solving Equation ABXC = D with Matrix Inverses

Nov 5, 2004 · Replies 4 · Nov 5, 2004

Replies: 4

Views: 2K

Undergrad How Can a^r = 1 mod N Be Expressed Differently If a and N Are Coprime?

Nov 4, 2004 · Replies 2 · Nov 4, 2004

Replies: 2

Views: 2K

Undergrad Have You Discovered This Recursive Formula for Sums of Powers?

Nov 4, 2004 · Replies 3 · Nov 4, 2004

Replies: 3

Views: 3K

Undergrad Why is Perpendicularity in 2D and 3D Important?

Nov 4, 2004 · Replies 5 · Nov 4, 2004

Replies: 5

Views: 3K

Graduate How to Deduce the Sum of Squares of Divisors from Canonical Representation?

Oct 27, 2004 · Replies 2 · Nov 4, 2004

Replies: 2

Views: 3K

Undergrad Solving AxB = (B-1A-1)-1: Inverse Matrix Proof

Nov 2, 2004 · Replies 2 · Nov 3, 2004

Replies: 2

Views: 12K

Undergrad Number of possible electoral college ties

Nov 1, 2004 · Replies 11 · Nov 2, 2004

Replies: 11

Views: 4K

Undergrad Coordinate transformation matrix?

Nov 1, 2004 · Replies 3 · Nov 2, 2004

Replies: 3

Views: 8K

Graduate Solve Laplace Expansion Determinant -2a,-2b,-2c,2p+x,2q+y,2r+z,3x,3y,3z

Oct 25, 2004 · Replies 2 · Nov 1, 2004

Replies: 2

Views: 3K

Graduate How Does Pi Squared Relate to Integer Pythagorean Triples?

Oct 25, 2004 · Replies 2 · Nov 1, 2004

Replies: 2

Views: 2K

Graduate A primality test for Fermat numbers faster than Pépin's test ?

Oct 26, 2004 · Replies 2 · Nov 1, 2004

Replies: 2

Views: 7K

Undergrad Is the Matrix A with Entries aij=min(i,j) Always Invertible?

Oct 25, 2004 · Replies 2 · Nov 1, 2004

Replies: 2

Views: 3K

Undergrad Vector Operations in Polar Coordinates?

Oct 28, 2004 · Replies 2 · Oct 29, 2004

Replies: 2

Views: 11K

Undergrad Division theoryand Prime Number theory

Oct 27, 2004 · Replies 3 · Oct 28, 2004

Replies: 3

Views: 13K

Graduate Generator redefined more rigorously

Oct 22, 2004 · Replies 14 · Oct 28, 2004

Replies: 14

Views: 3K

Undergrad Finding all solutions of Ax = y

Oct 20, 2004 · Replies 2 · Oct 28, 2004

Replies: 2

Views: 8K

Graduate How Can Gram-Schmidt Prove dim(w)=dim(V)-1?

Oct 26, 2004 · Replies 2 · Oct 27, 2004

Replies: 2

Views: 7K

Graduate How can we show that x^m is in a normal subgroup N of G if |G/N| = m?

Oct 20, 2004 · Replies 2 · Oct 27, 2004

Replies: 2

Views: 3K

High School Prime Factorization of 49 + 39 - MathFest 2004

Oct 27, 2004 · Replies 2 · Oct 27, 2004

Replies: 2

Views: 5K

Undergrad Proving Triangle Midpoint Sum Equals Side Length Sum

Oct 26, 2004 · Replies 3 · Oct 26, 2004

Replies: 3

Views: 4K

Undergrad An Algorithm to find a Prime Decompisition

Oct 19, 2004 · Replies 2 · Oct 26, 2004

Replies: 2

Views: 4K

Graduate What Does This Subspace Expression Mean?

Oct 24, 2004 · Replies 10 · Oct 26, 2004

Replies: 10

Views: 7K

Graduate Got a bizzare question, appreciate any hints

Oct 25, 2004 · Replies 3 · Oct 26, 2004

Replies: 3

Views: 3K

Graduate How Do Splitting Fields Relate to Each Other?

Oct 23, 2004 · Replies 5 · Oct 25, 2004

Replies: 5

Views: 4K

Graduate Proving Invertibility of Matrices: A Small Difference Makes a Big Impact

Oct 25, 2004 · Replies 2 · Oct 25, 2004

Replies: 2

Views: 2K

High School Solving a 4x4 Determinant for Math Projects

Oct 23, 2004 · Replies 4 · Oct 24, 2004

Replies: 4

Views: 12K

Undergrad What is the Basis for the Subspace V in R3 with the Equation x+2y+3z=0?

Oct 24, 2004 · Replies 2 · Oct 24, 2004

Replies: 2

Views: 3K

Graduate How Do Prime Numbers Divide Factorials?

Oct 17, 2004 · Replies 2 · Oct 24, 2004

Replies: 2

Views: 3K

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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