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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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Lin. transf. and linear independence

Feb 9, 2005 · Replies 2 · Feb 9, 2005

Replies: 2

Views: 2K

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

Feb 8, 2005 · Replies 5 · Feb 9, 2005

Replies: 5

Views: 3K

Learn How to Solve sin(nx)/n for Infinity with Expert Guidance"

Feb 7, 2005 · Replies 4 · Feb 9, 2005

Replies: 4

Views: 3K

Proving Algebraic Nature of Root 3 + Root 2

Feb 2, 2005 · Replies 2 · Feb 8, 2005

Replies: 2

Views: 2K

What is the significance of Rn and Rm in Calculus?

Feb 7, 2005 · Replies 4 · Feb 8, 2005

Replies: 4

Views: 6K

Linear Algebra Hw Help: Subset Independence & Dimension | C(R) Functions"

Jan 30, 2005 · Replies 10 · Feb 8, 2005

Replies: 10

Views: 2K

Proving the Intermediate Value Theorem in Higher Dimensions using Homeomorphisms

Dec 28, 2004 · Replies 10 · Feb 8, 2005

Replies: 10

Views: 5K

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

Feb 5, 2005 · Replies 3 · Feb 7, 2005

Replies: 3

Views: 5K

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

Feb 6, 2005 · Replies 2 · Feb 6, 2005

Replies: 2

Views: 2K

Merseinne Primes: Question from a Maths Dunce

Jan 19, 2005 · Replies 8 · Feb 6, 2005

Replies: 8

Views: 3K

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

Jan 24, 2005 · Replies 3 · Feb 5, 2005

Replies: 3

Views: 3K

Ripped Off: Paid $1 for a Free Bag?

Jan 27, 2005 · Replies 15 · Feb 4, 2005

Replies: 15

Views: 3K

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

Feb 3, 2005 · Replies 5 · Feb 4, 2005

Replies: 5

Views: 3K

Proving Inverses Exist in Finite Fields: A Common Challenge in Field Theory

Feb 2, 2005 · Replies 19 · Feb 3, 2005

Replies: 19

Views: 4K

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

Feb 3, 2005 · Replies 2 · Feb 3, 2005

Replies: 2

Views: 3K

Do different eigenvector algorithms yield different results?

Jan 31, 2005 · Replies 3 · Feb 1, 2005

Replies: 3

Views: 2K

Solving Gaussian Elimination Algorithm Problem (Matrices)

Jan 24, 2005 · Replies 2 · Jan 31, 2005

Replies: 2

Views: 5K

What is Hilbert Space and Why is it Important in Mathematics?

Jan 29, 2005 · Replies 5 · Jan 31, 2005

Replies: 5

Views: 4K

Independence Test Homework Problem Solution

Jan 29, 2005 · Replies 4 · Jan 31, 2005

Replies: 4

Views: 2K

Introductory Number Theory Books for High School Seniors

Dec 29, 2004 · Replies 12 · Jan 30, 2005

Replies: 12

Views: 5K

Row reduced matrix has coefficents

Jan 26, 2005 · Replies 2 · Jan 29, 2005

Replies: 2

Views: 9K

How Can I Interpolate Rotation Matrices for Skeletal Animation?

Jan 23, 2005 · Replies 2 · Jan 27, 2005

Replies: 2

Views: 11K

Representing a permutation, and a curiosity

Jan 25, 2005 · Replies 4 · Jan 27, 2005

Replies: 4

Views: 3K

Vector Space Solutions for Systems: Explained Here

Jan 26, 2005 · Replies 2 · Jan 26, 2005

Replies: 2

Views: 2K

Is Scalar Multiplication of Vectors Written Without Parentheses?

Jan 24, 2005 · Replies 3 · Jan 26, 2005

Replies: 3

Views: 6K

Infinetely many primes of the form 3n+1

Jan 23, 2005 · Replies 4 · Jan 25, 2005

Replies: 4

Views: 12K

What is the purpose of linear algebra in real life?

Dec 16, 2004 · Replies 20 · Jan 17, 2005

Replies: 20

Views: 6K

Another complex system of linear equations

Jan 17, 2005 · Replies 8 · Jan 17, 2005

Replies: 8

Views: 8K

Diagonalize a Matrix A - Normalize eigenvectors

Jan 16, 2005 · Replies 6 · Jan 16, 2005

Replies: 6

Views: 29K

How to Start Learning Lie Groups with Minimal Physics Background?

Jan 12, 2005 · Replies 2 · Jan 14, 2005

Replies: 2

Views: 3K

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

Jan 12, 2005 · Replies 3 · Jan 14, 2005

Replies: 3

Views: 4K

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

Jan 12, 2005 · Replies 4 · Jan 14, 2005

Replies: 4

Views: 3K

Anoter question on vector spaces an rationnal numbers

Dec 20, 2004 · Replies 39 · Jan 11, 2005

2

Replies: 39

Views: 7K

Finding Solutions to Complex Linear Systems

Jan 10, 2005 · Replies 3 · Jan 10, 2005

Replies: 3

Views: 3K

How do u show that a matrix is diagonizable?

Jan 2, 2005 · Replies 3 · Jan 8, 2005

Replies: 3

Views: 4K

What are the properties of subspaces?

Jan 6, 2005 · Replies 9 · Jan 6, 2005

Replies: 9

Views: 3K

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

Dec 1, 2004 · Replies 22 · Jan 6, 2005

Replies: 22

Views: 11K

Coordinates of vector to the base

Jan 3, 2005 · Replies 2 · Jan 5, 2005

Replies: 2

Views: 3K

Is the Collatz Problem Undecidable or Not?

Jan 1, 2005 · Replies 14 · Jan 4, 2005

Replies: 14

Views: 6K

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

Dec 28, 2004 · Replies 9 · Jan 2, 2005

Replies: 9

Views: 15K

Solving Linear Dynamical Systems with Eigenvectors and Eigenvalues

Jan 2, 2005 · Replies 15 · Jan 2, 2005

Replies: 15

Views: 3K

Finding Eigenvalues of an Arbitrary Matrix

Jan 2, 2005 · Replies 6 · Jan 2, 2005

Replies: 6

Views: 3K

System of linear congruences Help, please

Dec 26, 2004 · Replies 2 · Jan 2, 2005

Replies: 2

Views: 5K

Prove: Every Subfield of C Contains Rational Numbers

Dec 29, 2004 · Replies 11 · Dec 30, 2004

Replies: 11

Views: 5K

Is V \ U a Subspace of V? Examining the Conditions for Subspace Inclusion

Dec 27, 2004 · Replies 4 · Dec 28, 2004

Replies: 4

Views: 3K

Generalized Pell Equation and Primes

Dec 22, 2004 · Replies 6 · Dec 25, 2004

Replies: 6

Views: 6K

Solving Polynomials (mod p) Problems

Dec 15, 2004 · Replies 3 · Dec 22, 2004

Replies: 3

Views: 7K

Has Anyone Explored 3D Number Scattering?

Dec 7, 2004 · Replies 22 · Dec 21, 2004

Replies: 22

Views: 5K

Parallelogram Equality+Inner Product Spaces

Dec 21, 2004 · Replies 2 · Dec 21, 2004

Replies: 2

Views: 9K

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

Dec 12, 2004 · Replies 9 · Dec 21, 2004

Replies: 9

Views: 4K

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

Dec 20, 2004 · Replies 2 · Dec 20, 2004

Replies: 2

Views: 12K

Are There Multiple Solutions to this System of Linear Congruences?

Dec 16, 2004 · Replies 7 · Dec 20, 2004

Replies: 7

Views: 8K

How to Prove the Determinant of a Cosine Matrix?

Dec 13, 2004 · Replies 2 · Dec 20, 2004

Replies: 2

Views: 4K

Can a subgroup be mapped onto its parent group as a homomorphism?

Dec 19, 2004 · Replies 3 · Dec 19, 2004

Replies: 3

Views: 3K

Some clarification on upper triangular matrices please.

Dec 18, 2004 · Replies 2 · Dec 19, 2004

Replies: 2

Views: 6K

Finding Commuting Permutations in S_6 for alpha=(1 2 4 5)

Dec 5, 2004 · Replies 11 · Dec 17, 2004

Replies: 11

Views: 9K

Hilbert space and infinite norm vectors

Dec 17, 2004 · Replies 4 · Dec 17, 2004

Replies: 4

Views: 6K

How Do You Solve 4x=7 (mod 45) Using Remodularization Concepts?

Dec 16, 2004 · Replies 3 · Dec 17, 2004

Replies: 3

Views: 2K

Finding Elements of a Quotient Ring

Dec 16, 2004 · Replies 2 · Dec 16, 2004

Replies: 2

Views: 6K

Can Someone explain Dedikind cuts?

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

Replies: 11

Views: 5K

Solving Vector Spaces Problems with Calculus

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

Replies: 3

Views: 3K

A Short Course on Quantum Matrices: Understanding Notation Basics

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

Replies: 2

Views: 4K

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

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

2

Replies: 53

Views: 11K

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

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

Replies: 4

Views: 6K

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

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

Replies: 4

Views: 4K

How do I show that A is not diagonalizable?

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

Replies: 3

Views: 2K

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

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

Replies: 6

Views: 4K

How to Prove Zero Product Property for Rational Numbers?

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

Replies: 3

Views: 3K

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

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

Replies: 2

Views: 15K

LUB and Nested Interval Equivalancy

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

Replies: 5

Views: 5K

How Rademacher Derived His Formula for Partitioning Integers

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

Replies: 4

Views: 3K

Modulo arithmetic (?) question

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

Replies: 10

Views: 3K

Surjective and bijective mapping

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

Replies: 5

Views: 7K

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

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

Replies: 17

Views: 4K

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

Finding the eigenvalue for a given graph

Dec 8, 2004 · Replies 2 · Dec 8, 2004

Replies: 2

Views: 2K

Vectors Property: Necessary & Sufficient Conditions

Dec 1, 2004 · Replies 2 · Dec 8, 2004

Replies: 2

Views: 2K

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

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

Permutations and Transpositions problem help

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

Replies: 11

Views: 5K

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

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

Replies: 12

Views: 3K

What is the concept of injection and surjection?

Dec 5, 2004 · Replies 5 · Dec 6, 2004

Replies: 5

Views: 3K

Total potential energy in matrix

Dec 5, 2004 · Replies 2 · Dec 6, 2004

Replies: 2

Views: 5K

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

Dec 1, 2004 · Replies 2 · Dec 5, 2004

Replies: 2

Views: 2K

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

Dec 2, 2004 · Replies 3 · Dec 5, 2004

Replies: 3

Views: 4K

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

Dec 3, 2004 · Replies 2 · Dec 5, 2004

Replies: 2

Views: 3K

What is the connection between Diophantine equations and number theory?

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

Replies: 2

Views: 3K

Lie group (additional condition)

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

Replies: 2

Views: 2K

I need a proof for this binomial property.

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

Replies: 6

Views: 4K

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

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

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

Replies: 2

Views: 2K

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

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

Replies: 2

Views: 3K

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

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

Replies: 6

Views: 4K

Multiplication (powers) of fractions

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

Replies: 19

Views: 37K

Does Every Linear Operator Have a Nontrivial Invariant Subspace?

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

Replies: 6

Views: 7K

Proving F is Finite: A Perspective on Ring Homomorphisms

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

Replies: 3

Views: 5K

A bit of trouble with Galois groups

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

Replies: 2

Views: 3K

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

Solving a System of Equations with Matrix

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

Replies: 2

Views: 3K

Optimizing Integer Comparison without If Statements

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

Replies: 5

Views: 5K

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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