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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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What Are the Key Divisibility Rules and Counterexamples in Number Theory?

Jun 20, 2004 · Replies 5 · Jun 25, 2004

Replies: 5

Views: 3K

Understanding Theory: Solving Real Number Problems with Ease

Jun 24, 2004 · Replies 4 · Jun 24, 2004

Replies: 4

Views: 3K

Prove to me that the pythagorean triples

Jun 23, 2004 · Replies 11 · Jun 24, 2004

Replies: 11

Views: 4K

Can the GCD and LCM of [a,b] be proven to equal [ac,bc] with c>0?

Jun 22, 2004 · Replies 9 · Jun 23, 2004

Replies: 9

Views: 6K

What is the smallest possible positive real number?

Mar 23, 2004 · Replies 16 · Jun 21, 2004

Replies: 16

Views: 13K

Is the Product of Primes Significant in Number Theory?

Nov 15, 2003 · Replies 38 · Jun 20, 2004

2

Replies: 38

Views: 7K

How Do Addition and Multiplication Tables Work in Base -5?

Jun 19, 2004 · Replies 5 · Jun 20, 2004

Replies: 5

Views: 4K

Need help Proving quadriatic equation

Jun 19, 2004 · Replies 4 · Jun 20, 2004

Replies: 4

Views: 4K

Validate 10|z: 8 Cases to Consider

Jun 20, 2004 · Replies 6 · Jun 20, 2004

Replies: 6

Views: 3K

Is There a Contradiction in the Brain Teaser with Positive Integers x and y?

Jun 20, 2004 · Replies 2 · Jun 20, 2004

Replies: 2

Views: 2K

Solve Modular Math Problem: A,B→C

Jun 19, 2004 · Replies 7 · Jun 20, 2004

Replies: 7

Views: 3K

Is there yet a mystery about partitions?

Jun 6, 2004 · Replies 2 · Jun 19, 2004

Replies: 2

Views: 3K

Is the number of twin primes really infinite?

Jun 5, 2004 · Replies 6 · Jun 19, 2004

Replies: 6

Views: 6K

Solve x + y = Relatively Prime: Need Help

Jun 19, 2004 · Replies 3 · Jun 19, 2004

Replies: 3

Views: 2K

Discover an Original Identity with Merten's Function

May 5, 2004 · Replies 2 · Jun 19, 2004

Replies: 2

Views: 3K

What is the value of this infinite product?

Mar 30, 2004 · Replies 13 · Jun 18, 2004

Replies: 13

Views: 5K

Fractional Series which approach the square roots of prime numbers.

May 4, 2004 · Replies 2 · Jun 18, 2004

Replies: 2

Views: 5K

Help with Vector Space: Real Vector Space Explained

Jun 9, 2004 · Replies 12 · Jun 15, 2004

Replies: 12

Views: 9K

Looking for Online Document on SO(N)

Jun 10, 2004 · Replies 2 · Jun 14, 2004

Replies: 2

Views: 2K

Determinant = volume using rows.

Jun 6, 2004 · Replies 2 · Jun 14, 2004

Replies: 2

Views: 5K

Laplace Transform - How was it created?

Jun 10, 2004 · Replies 2 · Jun 11, 2004

Replies: 2

Views: 11K

Can f(n) equal f(x) in the sum of digits equation?

May 6, 2004 · Replies 5 · Jun 11, 2004

Replies: 5

Views: 9K

Proof: Numbers with repeating blocks of digits are rational

Jun 4, 2004 · Replies 7 · Jun 9, 2004

Replies: 7

Views: 5K

Compress 3D Objects Into 2 Dimensions?

Apr 15, 2004 · Replies 7 · Jun 9, 2004

Replies: 7

Views: 4K

Understanding Linear Equations and the Simplex Method for Function Optimization

May 22, 2004 · Replies 6 · Jun 8, 2004

Replies: 6

Views: 3K

Is This the Real Proof of Fermat's Last Theorem?

Jun 3, 2004 · Replies 7 · Jun 7, 2004

Replies: 7

Views: 3K

When is Matrix C Not Invertible?

Jun 5, 2004 · Replies 3 · Jun 5, 2004

Replies: 3

Views: 4K

Is There a General Method for Finding Full Reptend Primes?

Jun 4, 2004 · Replies 13 · Jun 4, 2004

Replies: 13

Views: 4K

Introducing Yourself to Compact and Non-Compact Lie Algebras

May 27, 2004 · Replies 2 · Jun 3, 2004

Replies: 2

Views: 3K

How Can Infinitely Many Integers Make n² + (n+1)² a Perfect Square?

May 5, 2004 · Replies 4 · May 30, 2004

Replies: 4

Views: 4K

Intergration: Algebra, Writing Equations of Lines

May 23, 2004 · Replies 2 · May 30, 2004

Replies: 2

Views: 3K

Is Wilson's Theorem Really a Proof?

Mar 6, 2004 · Replies 22 · May 30, 2004

Replies: 22

Views: 16K

Proving (n^4) + 4 is Composite for All n>1: The Odd n Case

Apr 19, 2004 · Replies 7 · May 27, 2004

Replies: 7

Views: 13K

Need Explination (linear Indpendance)

May 24, 2004 · Replies 3 · May 25, 2004

Replies: 3

Views: 7K

Circle composition operator / Jacobson Radical

May 11, 2004 · Replies 10 · May 24, 2004

Replies: 10

Views: 6K

Find Equation for Parabola-Help, Please?

May 12, 2004 · Replies 2 · May 19, 2004

Replies: 2

Views: 7K

Can This Mathematical Permutation Problem Be Generalized for Any 4n Terms?

May 2, 2004 · Replies 2 · May 17, 2004

Replies: 2

Views: 2K

Solving Complex Matrix Problems: Normality, Diagonality, and Unitary Matrices

May 17, 2004 · Replies 4 · May 17, 2004

Replies: 4

Views: 4K

Linear Transformation of s u + r V

May 13, 2004 · Replies 2 · May 17, 2004

Replies: 2

Views: 4K

Smallest Number Divisible by 2-10: Is it 7560?

May 11, 2004 · Replies 6 · May 13, 2004

Replies: 6

Views: 6K

Belian group A that is the direct sum of cyclic groups

May 11, 2004 · Replies 2 · May 12, 2004

Replies: 2

Views: 3K

Necessary and sufficient condition

May 9, 2004 · Replies 4 · May 10, 2004

Replies: 4

Views: 4K

Trouble understanding how to formulate rhis problem

May 9, 2004 · Replies 3 · May 10, 2004

Replies: 3

Views: 2K

Can the Polynomial g(x) Have a Solution Modulo Any Integer n?

May 6, 2004 · Replies 6 · May 10, 2004

Replies: 6

Views: 3K

Sufficiency of n eqs. for n unkwns.

May 7, 2004 · Replies 4 · May 9, 2004

Replies: 4

Views: 2K

Proving and Disproving a Mathematical Problem: Adding Numbers in Any Base

Apr 28, 2004 · Replies 10 · May 6, 2004

Replies: 10

Views: 3K

Some theorems regarding decimal representations

Apr 27, 2004 · Replies 2 · May 4, 2004

Replies: 2

Views: 2K

Anyone able to help with these vectors geometry and planes questions?

Apr 27, 2004 · Replies 2 · May 4, 2004

Replies: 2

Views: 3K

General Solutions for three-point parabola

Apr 26, 2004 · Replies 2 · May 3, 2004

Replies: 2

Views: 7K

Can the group of rational numbers be generated by a finite set of elements?

Apr 28, 2004 · Replies 7 · Apr 29, 2004

Replies: 7

Views: 15K

Some theorem regarding rational numbers

Apr 28, 2004 · Replies 6 · Apr 28, 2004

Replies: 6

Views: 5K

What are the ideals in various rings?

Apr 27, 2004 · Replies 6 · Apr 28, 2004

Replies: 6

Views: 5K

Finding the Line of Intersection for Two Planes

Apr 27, 2004 · Replies 2 · Apr 27, 2004

Replies: 2

Views: 14K

Understanding Vector Transformation with <1,-1> Translation - Explained

Apr 22, 2004 · Replies 3 · Apr 26, 2004

Replies: 3

Views: 3K

Relationship between Linear Algebra and Differential equations

Apr 21, 2004 · Replies 3 · Apr 23, 2004

Replies: 3

Views: 9K

Matrix M Formulation for Xn and Xn+1

Apr 19, 2004 · Replies 3 · Apr 23, 2004

Replies: 3

Views: 3K

Def.: Continuously Indexed Vector Basis?

Apr 16, 2004 · Replies 6 · Apr 22, 2004

Replies: 6

Views: 3K

How to solve an exponential ciphers?

Apr 9, 2004 · Replies 3 · Apr 20, 2004

Replies: 3

Views: 7K

How Do Units Determine Norm Values in Rings?

Apr 13, 2004 · Replies 2 · Apr 20, 2004

Replies: 2

Views: 5K

How to Solve for Integers Modulo n?

Apr 9, 2004 · Replies 4 · Apr 20, 2004

Replies: 4

Views: 4K

Why is 10 the Standard Base Number in Mathematics?

Mar 30, 2004 · Replies 15 · Apr 20, 2004

Replies: 15

Views: 4K

Understanding Group Orders: A Take Home Problem

Apr 17, 2004 · Replies 4 · Apr 19, 2004

Replies: 4

Views: 6K

Unitary: Are Det(A) & AdjointA=I Equivalent?

Apr 12, 2004 · Replies 29 · Apr 18, 2004

Replies: 29

Views: 6K

Prove any three vectors of R^3 are linear independent

Apr 17, 2004 · Replies 8 · Apr 18, 2004

Replies: 8

Views: 4K

Homogeneous Equation (easier question)

Apr 15, 2004 · Replies 2 · Apr 15, 2004

Replies: 2

Views: 6K

Homogenous Equation: Finding 'X' with Non-Invertible Matrix A | Solution Help

Apr 14, 2004 · Replies 3 · Apr 15, 2004

Replies: 3

Views: 3K

Find the area of the original parallelogram

Apr 6, 2004 · Replies 2 · Apr 14, 2004

Replies: 2

Views: 3K

Sums of digits of Perfect Squares

Apr 10, 2004 · Replies 25 · Apr 12, 2004

Replies: 25

Views: 20K

How Can You Partition Symmetry Groups Using the Multiplication Table Method?

Apr 8, 2004 · Replies 2 · Apr 12, 2004

Replies: 2

Views: 3K

Guassian elimination and Inverse Matrix

Feb 24, 2004 · Replies 3 · Apr 11, 2004

Replies: 3

Views: 7K

Geometric App's of Linear Algebra

Apr 8, 2004 · Replies 10 · Apr 10, 2004

Replies: 10

Views: 3K

What Is the Term for Decomposing Numbers into Additive Combinations?

Mar 25, 2004 · Replies 2 · Apr 9, 2004

Replies: 2

Views: 5K

Group Theory Basics: Where Can I Learn More?

Apr 23, 2003 · Replies 210 · Apr 8, 2004

8

Replies: 210

Views: 60K

Finding a Book on Basic Number Theory

Mar 31, 2004 · Replies 2 · Apr 7, 2004

Replies: 2

Views: 4K

Solve for n: Positive Integer Sequence with Greatest Divisor and LCM

Mar 30, 2004 · Replies 15 · Apr 6, 2004

Replies: 15

Views: 3K

Conjugacy in A_n: Rules & Resources

Apr 4, 2004 · Replies 9 · Apr 5, 2004

Replies: 9

Views: 5K

What Are the Non-abelian Groups of a Given Order?

Apr 4, 2004 · Replies 4 · Apr 5, 2004

Replies: 4

Views: 11K

Why Is a Matrix Not Invertible When Its Determinant Is Zero?

Mar 23, 2004 · Replies 4 · Apr 2, 2004

Replies: 4

Views: 34K

How Do I Solve a Quadratic Regression for a Helicopter Jump Trajectory?

Apr 2, 2004 · Replies 3 · Apr 2, 2004

Replies: 3

Views: 3K

Formulas For Linear Functions. Can Anyone Me Understand This Problem?

Mar 31, 2004 · Replies 3 · Mar 31, 2004

Replies: 3

Views: 4K

Square matrices, determinants and consistency

Mar 24, 2004 · Replies 2 · Mar 31, 2004

Replies: 2

Views: 19K

Prove That If rv = 0 Then Either r=0 or v=0

Mar 30, 2004 · Replies 5 · Mar 30, 2004

Replies: 5

Views: 12K

Anyone familiar with Peano' (or Grassman) algebra?

Mar 7, 2004 · Replies 5 · Mar 28, 2004

Replies: 5

Views: 4K

Proving the Only Solution to p is 3: A Simple Mathematical Proof

Mar 25, 2004 · Replies 5 · Mar 25, 2004

Replies: 5

Views: 3K

Solve the Mystery: What is 9 times 7?

Mar 20, 2004 · Replies 3 · Mar 23, 2004

Replies: 3

Views: 3K

Solving a 4x4 Matrix Determinant: Factor/Cofactor & Triangular Form

Mar 22, 2004 · Replies 3 · Mar 23, 2004

Replies: 3

Views: 16K

Proof of Normal Subgroup Thm- Alternative Strategies

Mar 18, 2004 · Replies 11 · Mar 21, 2004

Replies: 11

Views: 5K

Finding the Largest Known Prime: M^2 is the Answer

Mar 12, 2004 · Replies 2 · Mar 19, 2004

Replies: 2

Views: 3K

Calculating Value of Continued Fraction

Mar 19, 2004 · Replies 4 · Mar 19, 2004

Replies: 4

Views: 8K

Why do piecewise smooth function spaces require an infinite basis in PDEs?

Mar 11, 2004 · Replies 2 · Mar 18, 2004

Replies: 2

Views: 3K

What Defines an Equivalence Relation?

Feb 29, 2004 · Replies 27 · Mar 17, 2004

Replies: 27

Views: 9K

Proving t(n) Divisible by 3 Implies n is Divisible by 3

Mar 14, 2004 · Replies 6 · Mar 16, 2004

Replies: 6

Views: 3K

Geometric Progression of Prime Numbers

Feb 1, 2004 · Replies 11 · Mar 15, 2004

Replies: 11

Views: 6K

Is the zeta function a complex mapping onto the infinite sum of 1/j^s terms?

Mar 15, 2004 · Replies 2 · Mar 15, 2004

Replies: 2

Views: 7K

How to Calculate a 3x3 Rotation Matrix around a Given Axis?

Mar 14, 2004 · Replies 5 · Mar 15, 2004

Replies: 5

Views: 14K

Solving the Puzzle: Ann and Mary's Ages

Mar 6, 2004 · Replies 2 · Mar 13, 2004

Replies: 2

Views: 3K

What is the Largest Integer Factored into Two Primes?

Mar 7, 2004 · Replies 5 · Mar 12, 2004

Replies: 5

Views: 3K

Singular Matrices: Disadvantages, Practical Use & Mass Quantization

Mar 9, 2004 · Replies 12 · Mar 10, 2004

Replies: 12

Views: 5K

Different coordinate system to sketch (x-2y)=sin(pi(x+y))

Feb 25, 2004 · Replies 2 · Mar 9, 2004

Replies: 2

Views: 4K

Man Cashes Cheque: Solve Assumptions to get Amount

Mar 7, 2004 · Replies 2 · Mar 8, 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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