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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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Can Ulam's Spiral Theory Be Enhanced with a Double Spiral Approach?

Sep 26, 2004 · Replies 2 · Sep 26, 2004

Replies: 2

Views: 3K

Is There a Hidden Pattern in Exponentiation Operations on Three Natural Numbers?

Sep 21, 2004 · Replies 8 · Sep 26, 2004

Replies: 8

Views: 4K

Prove Polarization Formula in Complex Vector Space

Sep 18, 2004 · Replies 2 · Sep 25, 2004

Replies: 2

Views: 2K

Is There a Mistake in Theorem 4.28 on Page 177 of Byron & Fuller's Book?

Sep 9, 2004 · Replies 2 · Sep 23, 2004

Replies: 2

Views: 3K

Prove Linear Independence of {u_1,u_2,...,u_k} for k=2,3,...,n-1

Sep 23, 2004 · Replies 7 · Sep 23, 2004

Replies: 7

Views: 2K

Showing Two Groups are Isomorphic

Aug 3, 2004 · Replies 32 · Sep 23, 2004

2

Replies: 32

Views: 24K

What Makes the Negative of a Dedekind Cut Not a Dedekind Cut?

Sep 19, 2004 · Replies 8 · Sep 23, 2004

Replies: 8

Views: 5K

Interesting problem with possible solution

Sep 22, 2004 · Replies 7 · Sep 23, 2004

Replies: 7

Views: 3K

Basis for the intersection of two spans

Aug 18, 2004 · Replies 2 · Sep 23, 2004

Replies: 2

Views: 24K

Finding a Formula for Sum of Series: 1^2 - 3^2 + 5^2 - 7^2 +...

Sep 17, 2004 · Replies 19 · Sep 23, 2004

Replies: 19

Views: 4K

What is the GCD of (a + b, a - b)?

Sep 18, 2004 · Replies 15 · Sep 23, 2004

Replies: 15

Views: 10K

How Much Force Does a Rope Exert on a Car in This Scenario?

Sep 21, 2004 · Replies 2 · Sep 22, 2004

Replies: 2

Views: 3K

How Can a Polynomial's Relationship With Its Derivative Indicate Multiple Roots?

May 6, 2004 · Replies 9 · Sep 21, 2004

Replies: 9

Views: 3K

Linear Supply Equation for a Commodity: Solving for Unknown Variables

Sep 14, 2004 · Replies 2 · Sep 21, 2004

Replies: 2

Views: 2K

Proof: x^n + 1 is Valid for Odd n".

Sep 19, 2004 · Replies 6 · Sep 21, 2004

Replies: 6

Views: 3K

Frustrating step in a proof - basic abstract algebra

Sep 14, 2004 · Replies 2 · Sep 21, 2004

Replies: 2

Views: 3K

Prime Numbers in Set S: Is 2*p>n?

Sep 19, 2004 · Replies 4 · Sep 20, 2004

Replies: 4

Views: 3K

Computing Distances: Evaluating Sums in Polynomials

Sep 16, 2004 · Replies 3 · Sep 20, 2004

Replies: 3

Views: 2K

Proving Subspace of Continuous Functions with Integral = 0

Sep 19, 2004 · Replies 2 · Sep 19, 2004

Replies: 2

Views: 2K

Is -1 Considered a Prime Number in Mathematical Discussions?

Jul 22, 2004 · Replies 13 · Sep 19, 2004

Replies: 13

Views: 4K

Is the Prime Numbers Function f(n) = 3^(n)+2 Always Prime?

Aug 10, 2004 · Replies 11 · Sep 19, 2004

Replies: 11

Views: 4K

Three-Way Arrays: Algebra Basics Explained

Sep 14, 2004 · Replies 12 · Sep 19, 2004

Replies: 12

Views: 3K

What is the Equation for a Series of Numbers with a Repeating Pattern?

Sep 19, 2004 · Replies 2 · Sep 19, 2004

Replies: 2

Views: 2K

Trouble w/ Maximal Principle (Zorn's Lemma)

Sep 13, 2004 · Replies 9 · Sep 19, 2004

Replies: 9

Views: 3K

What is e? Understanding the Eularian Constant and Its Applications

Jul 13, 2004 · Replies 21 · Sep 18, 2004

Replies: 21

Views: 8K

More algebraic geometry questions

Sep 9, 2004 · Replies 43 · Sep 18, 2004

2

Replies: 43

Views: 9K

Solving for Recurring Numbers: Techniques and Applications

Sep 18, 2004 · Replies 6 · Sep 18, 2004

Replies: 6

Views: 5K

What is the Spectrum of the Ring of Continuous Functions Over Rn?

Jun 27, 2004 · Replies 38 · Sep 18, 2004

2

Replies: 38

Views: 10K

Solving for Generators in Abelian Groups with Multiple Relations

May 17, 2004 · Replies 3 · Sep 17, 2004

Replies: 3

Views: 3K

Symmetries of a Regular Quindecagon: Order & Classification

Aug 11, 2004 · Replies 2 · Sep 17, 2004

Replies: 2

Views: 3K

Understanding Upper Triangular, Lower, and Diagonal Matrices

Aug 27, 2004 · Replies 3 · Sep 17, 2004

Replies: 3

Views: 3K

The Origin & History of Ring & Field: Who Invented Them?

Sep 10, 2004 · Replies 3 · Sep 17, 2004

Replies: 3

Views: 3K

Is there a misprint in this group theory exercise?

Jun 24, 2004 · Replies 22 · Sep 17, 2004

Replies: 22

Views: 4K

Calculating the Second Norm of a Matrix: Formula and Explanation

Aug 26, 2004 · Replies 2 · Sep 17, 2004

Replies: 2

Views: 12K

Proving the Span of u_1, u_2, ..., u_k and Av

Sep 16, 2004 · Replies 3 · Sep 17, 2004

Replies: 3

Views: 3K

Proving Spanning Sets in Vector Spaces

Aug 30, 2004 · Replies 15 · Sep 17, 2004

Replies: 15

Views: 4K

How Can We Automate Matrix Inversion for Matrices Near the Identity?

Sep 17, 2003 · Replies 8 · Sep 17, 2004

Replies: 8

Views: 44K

Cosets are either equal or disjoint

Jul 17, 2004 · Replies 12 · Sep 17, 2004

Replies: 12

Views: 7K

Euler Circuits and Vertices of Even Degree: Proof and Counter-Proof

Sep 13, 2004 · Replies 2 · Sep 17, 2004

Replies: 2

Views: 5K

Is |a| a Factor of |p0| in a General Polynomial of Degree n?

Jun 20, 2004 · Replies 5 · Sep 17, 2004

Replies: 5

Views: 3K

How Do You Find a Basis for the Nullspace When the First Column Is All Zeroes?

Sep 9, 2004 · Replies 2 · Sep 17, 2004

Replies: 2

Views: 6K

What is the cocycle condition in deRham cohomology?

Apr 15, 2004 · Replies 21 · Sep 16, 2004

Replies: 21

Views: 6K

Why is sin(2*pi/7) a Non-Constructible Number?

Apr 28, 2004 · Replies 2 · Sep 16, 2004

Replies: 2

Views: 5K

Find Perpendicular Bisector of Line AB (2,3) & (0,6)

Sep 16, 2004 · Replies 4 · Sep 16, 2004

Replies: 4

Views: 3K

How to solve Pell's equation using Alpertron's online calculator

Aug 2, 2004 · Replies 10 · Sep 9, 2004

Replies: 10

Views: 19K

How to Code a Vandermonde Matrix Inverse in Java?

Sep 7, 2004 · Replies 3 · Sep 8, 2004

Replies: 3

Views: 3K

I wont to learn the logic behind a determinant

Sep 4, 2004 · Replies 4 · Sep 5, 2004

Replies: 4

Views: 4K

Intersection of disjoint SETS is empty

Sep 1, 2004 · Replies 5 · Sep 2, 2004

Replies: 5

Views: 3K

Calculating Vector Magnitudes by Breaking Down Components

Aug 30, 2004 · Replies 5 · Aug 31, 2004

Replies: 5

Views: 30K

Best introductory book to senior algebra

Jun 7, 2004 · Replies 4 · Aug 30, 2004

Replies: 4

Views: 3K

Help solving a system of linear equations

Aug 26, 2004 · Replies 5 · Aug 28, 2004

Replies: 5

Views: 3K

Splitting a Matrix with Choleski Method: A Simple Example

Aug 20, 2004 · Replies 2 · Aug 28, 2004

Replies: 2

Views: 3K

How to determine the base of a Number given a problem?

Aug 23, 2004 · Replies 3 · Aug 23, 2004

Replies: 3

Views: 19K

Splitting a Square Matrix into Lower/Upper Triangular Matrices

Aug 18, 2004 · Replies 8 · Aug 21, 2004

Replies: 8

Views: 6K

Is pi+e Algebraic? Debunking the Mystery

Aug 18, 2004 · Replies 4 · Aug 18, 2004

Replies: 4

Views: 9K

What is the ratio of singular to non-singular matrices?

Aug 15, 2004 · Replies 10 · Aug 17, 2004

Replies: 10

Views: 4K

Are These Two Equations Linearly Independent?

May 25, 2004 · Replies 7 · Aug 16, 2004

Replies: 7

Views: 4K

Help with making an orthonormal basis

Jun 22, 2004 · Replies 4 · Aug 16, 2004

Replies: 4

Views: 6K

Ideas on what this transformation is doing?

Jun 23, 2004 · Replies 7 · Aug 15, 2004

Replies: 7

Views: 2K

How Can I Generate Two 1024 Bit Prime Numbers Using the AKS Primality Test?

Aug 13, 2004 · Replies 12 · Aug 15, 2004

Replies: 12

Views: 5K

What is the root between -3 and -2 for the equation y^3 - 3y + 4 = 0?

Aug 13, 2004 · Replies 3 · Aug 14, 2004

Replies: 3

Views: 2K

How Many Distinct Islands Can Exist in an nxn Grid with Multiple Colors?

Jul 25, 2004 · Replies 2 · Aug 11, 2004

Replies: 2

Views: 3K

Linear algebra book and other questions

Jul 21, 2004 · Replies 3 · Aug 10, 2004

Replies: 3

Views: 4K

Help with prime factorization proof

Feb 29, 2004 · Replies 9 · Aug 6, 2004

Replies: 9

Views: 9K

Solve this Math Problem: Find the Last Two/Three Digits of 3^3^3^3

May 11, 2004 · Replies 5 · Aug 5, 2004

Replies: 5

Views: 6K

Terms for Reaching 10^57 in a Series?

Aug 4, 2004 · Replies 3 · Aug 5, 2004

Replies: 3

Views: 9K

What are Some Challenging Number Theory Problems?

Jul 17, 2004 · Replies 8 · Aug 3, 2004

Replies: 8

Views: 5K

Solve Difficult Math Equation - SuperSamuraiStar

Jul 2, 2004 · Replies 6 · Aug 3, 2004

Replies: 6

Views: 5K

Solve Complicated Partial Fractions Questions

May 23, 2004 · Replies 9 · Aug 3, 2004

Replies: 9

Views: 4K

Number Theory ebooks: Free Fundamental Downloads

Jul 11, 2004 · Replies 5 · Jul 30, 2004

Replies: 5

Views: 4K

Finding Polynomials with Specific Properties: How Do I Do That?

Jul 28, 2004 · Replies 8 · Jul 29, 2004

Replies: 8

Views: 6K

What Are Alternative Applications of Linear Systems in Physics?

Jul 14, 2004 · Replies 2 · Jul 27, 2004

Replies: 2

Views: 4K

Please, some help on the 36-officers problem

Jul 24, 2004 · Replies 3 · Jul 26, 2004

Replies: 3

Views: 4K

Find Prime Double Pairs: Frequency & Infinity

Jul 21, 2004 · Replies 3 · Jul 22, 2004

Replies: 3

Views: 4K

Monotone convergence theory

Jul 21, 2004 · Replies 2 · Jul 22, 2004

Replies: 2

Views: 6K

3D graphics: finding optimal view of a scene with constraints

Jul 14, 2004 · Replies 3 · Jul 21, 2004

Replies: 3

Views: 4K

Looking for a good abstract book

May 13, 2004 · Replies 7 · Jul 20, 2004

Replies: 7

Views: 4K

I proving if a + a = 0 then a = 0

Jul 13, 2004 · Replies 2 · Jul 20, 2004

Replies: 2

Views: 3K

Finding riccati solution of A*X+A'*X+X*W*X+Q

Jul 6, 2004 · Replies 6 · Jul 12, 2004

Replies: 6

Views: 3K

How Can You Prove the Divisibility of 2x + 3y and 9x + 5y by 17?

Jul 8, 2004 · Replies 2 · Jul 8, 2004

Replies: 2

Views: 5K

How many possibilities are there to get 144

Jul 6, 2004 · Replies 5 · Jul 7, 2004

Replies: 5

Views: 3K

Can the Chinese Remainder Theorem be Used to Solve Systems of Linear Equations?

Mar 1, 2004 · Replies 2 · Jul 6, 2004

Replies: 2

Views: 3K

Inverse chinese remainder theorem

Feb 27, 2004 · Replies 9 · Jul 6, 2004

Replies: 9

Views: 9K

Proving gcd(a,n)=(a-1,n)=1 and its implications on mod calculations

Jul 5, 2004 · Replies 5 · Jul 6, 2004

Replies: 5

Views: 4K

Are My Congruence Calculations Correct?

Jul 3, 2004 · Replies 16 · Jul 5, 2004

Replies: 16

Views: 6K

7-million digit prime number discovered

Jun 4, 2004 · Replies 11 · Jul 5, 2004

Replies: 11

Views: 5K

No same factor theory inference by hey.like

Jul 3, 2004 · Replies 2 · Jul 5, 2004

Replies: 2

Views: 2K

Can You Solve the Real Challenge?

Jul 4, 2004 · Replies 3 · Jul 4, 2004

Replies: 3

Views: 3K

Does the Prime Factorial Conjecture Hold True for All Primes?

Jun 28, 2004 · Replies 3 · Jul 4, 2004

Replies: 3

Views: 7K

The Poincare Conjecture *Kinda long*

May 24, 2004 · Replies 3 · Jul 3, 2004

Replies: 3

Views: 5K

Understanding Reduced Residue Systems Mod 7: Can You Help?

Jun 30, 2004 · Replies 16 · Jul 3, 2004

Replies: 16

Views: 6K

Is there a relationship between these numbers from the Phi function?

Jul 2, 2004 · Replies 4 · Jul 2, 2004

Replies: 4

Views: 4K

Square matrix where the coefficients of the diagonal are 1

Jun 24, 2004 · Replies 2 · Jul 1, 2004

Replies: 2

Views: 5K

Modular Math Problem: What Is the Largest n?

May 11, 2004 · Replies 7 · Jun 30, 2004

Replies: 7

Views: 4K

Can Any Integral Weight Up to 121 Ounces Be Measured with Five Specific Weights?

Feb 12, 2004 · Replies 3 · Jun 30, 2004

Replies: 3

Views: 6K

Least Possible Sum of Recipricols of Two Positive Ints = 9

May 18, 2004 · Replies 6 · Jun 30, 2004

Replies: 6

Views: 3K

What Are the Most Fascinating Aspects of Purely Theoretical Mathematics?

Dec 2, 2003 · Replies 8 · Jun 29, 2004

Replies: 8

Views: 6K

Help Needed: Prime, Square & 0s - Seeking Direction

Jun 26, 2004 · Replies 8 · Jun 29, 2004

Replies: 8

Views: 2K

Are All Even Perfect Numbers Also Triangular Numbers?

Jun 27, 2004 · Replies 3 · Jun 29, 2004

Replies: 3

Views: 2K

Modulo and congruencies in class

Jun 27, 2004 · Replies 2 · Jun 27, 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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