Menu

Navigation

More options

Style variation

Contact us

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.

Filters

Exterior Algebra Tutorials - Differentials & Wedge Products

Dec 7, 2005 · Replies 3 · Dec 11, 2005

Replies: 3

Views: 4K

What Are Subspaces in Linear Spaces and How Are They Defined?

Dec 9, 2005 · Replies 14 · Dec 11, 2005

Replies: 14

Views: 3K

Power series to find the inverse of any function in Z_2[x]?

Dec 5, 2005 · Replies 14 · Dec 9, 2005

Replies: 14

Views: 4K

Mathlab and least square problem

Dec 3, 2005 · Replies 4 · Dec 8, 2005

Replies: 4

Views: 3K

Bounding pi(n): Dusart's 1999 Extension of Rosser's Theorem

Nov 17, 2005 · Replies 9 · Dec 7, 2005

Replies: 9

Views: 4K

Proving m+1 is a Perfect Square when m/8 is a Triangular Number

Dec 3, 2005 · Replies 8 · Dec 6, 2005

Replies: 8

Views: 3K

Understanding Faulhaber's Formula for Sum of Powers of n Integers

Dec 4, 2005 · Replies 1 · Dec 5, 2005

Replies: 1

Views: 3K

Counting Invertible Matrices in GL(3, Z_2)

Dec 4, 2005 · Replies 1 · Dec 4, 2005

Replies: 1

Views: 5K

Can Computers Solve Transcendental Equations?

Dec 4, 2005 · Replies 2 · Dec 4, 2005

Replies: 2

Views: 7K

Can Two Elevators with Different Periods Meet on the Same Floor?

Dec 4, 2005 · Replies 1 · Dec 4, 2005

Replies: 1

Views: 3K

Is f(x) = (x^3-2) irreducible over Z_p when 3 does not divide p-1?

Dec 3, 2005 · Replies 2 · Dec 3, 2005

Replies: 2

Views: 2K

Proving Abelian Group with Numbers and Operations

Nov 29, 2005 · Replies 6 · Dec 2, 2005

Replies: 6

Views: 3K

Congruences of (x^n-2) and its factors

Dec 1, 2005 · Replies 9 · Dec 1, 2005

Replies: 9

Views: 3K

Practical pseudoprimality testing

Dec 1, 2005 · Replies 4 · Dec 1, 2005

Replies: 4

Views: 3K

Cyclic Abelian Groups: True for All Cases?

Nov 28, 2005 · Replies 5 · Dec 1, 2005

Replies: 5

Views: 7K

Solving Complex Problems Without Expansion

Nov 30, 2005 · Replies 2 · Nov 30, 2005

Replies: 2

Views: 3K

Proving a Continuing Series: Methods

Nov 30, 2005 · Replies 3 · Nov 30, 2005

Replies: 3

Views: 2K

Properties of Composites Composed of Two Odd Prime Factors

Nov 21, 2005 · Replies 13 · Nov 29, 2005

Replies: 13

Views: 5K

What is "Modding Out by A" in R/A?

Nov 22, 2005 · Replies 4 · Nov 27, 2005

Replies: 4

Views: 4K

What is the Notation for Adjoints in Matrices?

Nov 20, 2005 · Replies 14 · Nov 24, 2005

Replies: 14

Views: 6K

Is 'Number Theory with Computer Applications' a Recommended Book for Beginners?

Aug 15, 2005 · Replies 29 · Nov 24, 2005

Replies: 29

Views: 19K

What is a good introductory textbook for Number Theory at the university level?

Oct 7, 2005 · Replies 2 · Nov 23, 2005

Replies: 2

Views: 4K

Have Unusual Theorems on Vector Spaces and Semigroups Been Explored?

Nov 22, 2005 · Replies 5 · Nov 23, 2005

Replies: 5

Views: 12K

Could Riemann Hypothesis be completely false?

Nov 3, 2005 · Replies 20 · Nov 22, 2005

Replies: 20

Views: 5K

Preadditive categories are all Abelian

Nov 18, 2005 · Replies 16 · Nov 22, 2005

Replies: 16

Views: 5K

Reduced Homology: Modding Z(+)Z & Zeroth Homology

Nov 19, 2005 · Replies 3 · Nov 22, 2005

Replies: 3

Views: 4K

Euler's Method of proving primes r infinite

Nov 19, 2005 · Replies 4 · Nov 21, 2005

Replies: 4

Views: 7K

The Diagonal Method: Proving Sets are Infinite

Nov 18, 2005 · Replies 5 · Nov 21, 2005

Replies: 5

Views: 3K

Proving b>(m+1)^2 for Perfect Square Conditions

Nov 19, 2005 · Replies 6 · Nov 21, 2005

Replies: 6

Views: 3K

Can n choose k be proven as a natural number without using induction?

Oct 29, 2005 · Replies 18 · Nov 19, 2005

Replies: 18

Views: 8K

What Are Dummy Variables and How Are They Used?

Nov 11, 2005 · Replies 7 · Nov 19, 2005

Replies: 7

Views: 14K

Is My Homemade Encryption Method Secure Enough for Real-World Use?

Nov 16, 2005 · Replies 6 · Nov 18, 2005

Replies: 6

Views: 2K

Is X*a#/X*b# Equal to a%/b%?

Nov 18, 2005 · Replies 1 · Nov 18, 2005

Replies: 1

Views: 3K

Can Pi be Constructed on a Number Line Using Non-Traditional Tools?

Nov 9, 2005 · Replies 7 · Nov 18, 2005

Replies: 7

Views: 18K

Can Pi be Used as a Random Number Generator for Proving Normality?

Nov 16, 2005 · Replies 3 · Nov 16, 2005

Replies: 3

Views: 4K

Powers of cycles? Orders of elements?

Nov 16, 2005 · Replies 1 · Nov 16, 2005

Replies: 1

Views: 2K

Is it possible to show that so(4) is equal to su(2) direct sum su(2)?

Nov 13, 2005 · Replies 9 · Nov 16, 2005

Replies: 9

Views: 8K

Finding Perfect Squares of n Factored as a^4*b^3*c^7

Nov 14, 2005 · Replies 3 · Nov 16, 2005

Replies: 3

Views: 2K

Are There Prime Factors of the Same Form for Integers of Form 3n+2?

Nov 15, 2005 · Replies 7 · Nov 15, 2005

Replies: 7

Views: 3K

General how to find the eigenvectors/values

Nov 14, 2005 · Replies 4 · Nov 15, 2005

Replies: 4

Views: 3K

Interesting problem from my analysis class

Nov 1, 2005 · Replies 6 · Nov 14, 2005

Replies: 6

Views: 3K

How to calculate the number of prime factors of 360?

Nov 12, 2005 · Replies 4 · Nov 14, 2005

Replies: 4

Views: 2K

Any Good Literature or Books on Number Theory

Nov 11, 2005 · Replies 4 · Nov 11, 2005

Replies: 4

Views: 11K

GNFS Factorization of RSA640 by Franke et al.

Nov 8, 2005 · Replies 12 · Nov 9, 2005

Replies: 12

Views: 4K

Understanding the Odd Permutation Product Mystery

Nov 7, 2005 · Replies 10 · Nov 9, 2005

Replies: 10

Views: 15K

Understanding Hilbert Space: Representing & Calculating Length of Functions

Nov 2, 2005 · Replies 15 · Nov 8, 2005

Replies: 15

Views: 5K

N elevators serving M floors most efficiently

Oct 6, 2005 · Replies 4 · Nov 7, 2005

Replies: 4

Views: 4K

Is there an explanation for why i^i is a real number?

Nov 2, 2005 · Replies 3 · Nov 6, 2005

Replies: 3

Views: 12K

Do All Small Colimits Exist in Algebra?

Oct 30, 2005 · Replies 8 · Nov 3, 2005

Replies: 8

Views: 3K

Is There Evidence Supporting Multiple Twin Primes in Specified Intervals?

Nov 2, 2005 · Replies 3 · Nov 2, 2005

Replies: 3

Views: 4K

What Are the Various Applications of Matrices Beyond Solving Equations?

Oct 29, 2005 · Replies 7 · Nov 2, 2005

Replies: 7

Views: 3K

Please recommend textbook for self study

Sep 12, 2005 · Replies 15 · Nov 1, 2005

Replies: 15

Views: 6K

Understanding Prevarieties and Affine Varieties in Projective Space

Oct 5, 2005 · Replies 7 · Nov 1, 2005

Replies: 7

Views: 5K

Understanding Quotient Fields and Functors in Commutative Algebra

Oct 17, 2005 · Replies 10 · Nov 1, 2005

Replies: 10

Views: 5K

I've just come across one-forms for the first time

Oct 22, 2005 · Replies 25 · Nov 1, 2005

Replies: 25

Views: 6K

A little help with Linear Transformations

Oct 30, 2005 · Replies 2 · Nov 1, 2005

Replies: 2

Views: 2K

What exactly is Abstract Algebra?

Oct 30, 2005 · Replies 9 · Nov 1, 2005

Replies: 9

Views: 9K

Algebra for Homology: A Resource Guide

Oct 30, 2005 · Replies 1 · Nov 1, 2005

Replies: 1

Views: 2K

The Epstein Zeta Function: Definition, Zeros, and Functional Equation Explained

Nov 1, 2005 · Replies 2 · Nov 1, 2005

Replies: 2

Views: 5K

Proving Twin Primes with n and n+2 mod n(n+2)

Oct 31, 2005 · Replies 4 · Oct 31, 2005

Replies: 4

Views: 2K

Thinking about matrices/polynomials

Oct 30, 2005 · Replies 2 · Oct 31, 2005

Replies: 2

Views: 3K

Notation of ln_2(k): Logarithmic or Trig Functions?

Oct 29, 2005 · Replies 2 · Oct 30, 2005

Replies: 2

Views: 2K

Quick question on a group definition

Oct 29, 2005 · Replies 7 · Oct 29, 2005

Replies: 7

Views: 2K

A proof of Riemann hypothesis (but of course the snobbish journals don,t want

Oct 28, 2005 · Replies 11 · Oct 29, 2005

Replies: 11

Views: 4K

Linear Regression, Linear Least Squares, Least Squares, Non-linear Least Squares

Oct 21, 2005 · Replies 4 · Oct 27, 2005

Replies: 4

Views: 11K

Is the Boundary of an Open Set Always Its Complement?

Oct 24, 2005 · Replies 13 · Oct 27, 2005

Replies: 13

Views: 6K

Grade Iterated Möbius Transformations Essay | Any University

Aug 25, 2005 · Replies 14 · Oct 27, 2005

Replies: 14

Views: 4K

Why is scalar multiplication on vector spaces not commutative?

Oct 15, 2005 · Replies 3 · Oct 25, 2005

Replies: 3

Views: 13K

Proving Linear Transformation of Polynomials: Let Px be union of all polynomials

Oct 24, 2005 · Replies 3 · Oct 25, 2005

Replies: 3

Views: 3K

Example of Non-Square Relatively Prime Integers w/ Square Product

Oct 24, 2005 · Replies 2 · Oct 24, 2005

Replies: 2

Views: 3K

Proof of gcd and lcm properties for prime factorizations

Oct 24, 2005 · Replies 2 · Oct 24, 2005

Replies: 2

Views: 5K

Can the Null Space of a Matrix Be the Same as Its Transpose?

Oct 23, 2005 · Replies 1 · Oct 24, 2005

Replies: 1

Views: 10K

How Can I Access Online Textbooks for University Level Math Courses?

Sep 4, 2005 · Replies 5 · Oct 23, 2005

Replies: 5

Views: 3K

How Can You Easily Square Big Numbers Without a Calculator?

Oct 19, 2005 · Replies 2 · Oct 22, 2005

Replies: 2

Views: 3K

Fibonacci Phi - The Golden Ratio

Oct 11, 2005 · Replies 19 · Oct 22, 2005

Replies: 19

Views: 9K

Why people need to define determinant ?

Oct 8, 2005 · Replies 2 · Oct 17, 2005

Replies: 2

Views: 3K

Does (a^m^2 + 1) Divide (a^n^2 - 1) for n > m?

Oct 17, 2005 · Replies 1 · Oct 17, 2005

Replies: 1

Views: 3K

Examples of Finite Non-Commutative Rings

Oct 9, 2005 · Replies 2 · Oct 9, 2005

Replies: 2

Views: 3K

Mathematics Journal, Proof for

Sep 26, 2005 · Replies 4 · Oct 9, 2005

Replies: 4

Views: 2K

Is 1 Really Equal to .9999999999999999999?

Oct 7, 2005 · Replies 3 · Oct 8, 2005

Replies: 3

Views: 13K

Vectors and the Menelaus Theorem

Oct 6, 2005 · Replies 2 · Oct 7, 2005

Replies: 2

Views: 3K

Abstract Algebra - Compositions

Oct 2, 2005 · Replies 2 · Oct 6, 2005

Replies: 2

Views: 2K

Classification of diagonalizable matrices

Sep 27, 2005 · Replies 7 · Oct 6, 2005

Replies: 7

Views: 4K

God, I hate Number Theory Proofs

Oct 2, 2005 · Replies 6 · Oct 5, 2005

Replies: 6

Views: 10K

Prove that that every symmetric real matrix is diagonalizable?

Oct 3, 2005 · Replies 1 · Oct 4, 2005

Replies: 1

Views: 3K

Does Ax=Bx for All Vectors Guarantee A=B for Matrices?

Oct 2, 2005 · Replies 3 · Oct 4, 2005

Replies: 3

Views: 18K

Quick Clarification Quite Curious

Oct 3, 2005 · Replies 1 · Oct 3, 2005

Replies: 1

Views: 2K

Prove if a ring has a unity, then it is unique

Oct 2, 2005 · Replies 4 · Oct 2, 2005

Replies: 4

Views: 5K

Represent a matrix on the (x,y)-plane

Oct 2, 2005 · Replies 2 · Oct 2, 2005

Replies: 2

Views: 2K

Reduced row echelon form of matrix

Sep 26, 2005 · Replies 1 · Oct 1, 2005

Replies: 1

Views: 10K

Prime number counting function with error O(x^e)

Sep 25, 2005 · Replies 27 · Sep 30, 2005

Replies: 27

Views: 6K

Explore Number Theory and Geometry with Mathematics Problem Explorer Book

Sep 29, 2005 · Replies 2 · Sep 30, 2005

Replies: 2

Views: 3K

Sieving for Primes - A Program to Find Primes in Any Range

Aug 24, 2005 · Replies 9 · Sep 29, 2005

Replies: 9

Views: 3K

Solution needed 4 a very good problem

Sep 29, 2005 · Replies 8 · Sep 29, 2005

Replies: 8

Views: 2K

Is the Empty Set a Valid Vector Space? A Closer Look at the Ten Axioms

Aug 3, 2005 · Replies 33 · Sep 29, 2005

2

Replies: 33

Views: 20K

A Question in Linear Tranformations

Sep 26, 2005 · Replies 2 · Sep 27, 2005

Replies: 2

Views: 3K

Equation of a relation that appears to be its own reciprocal?

Sep 25, 2005 · Replies 3 · Sep 26, 2005

Replies: 3

Views: 2K

How to Find a K for Prime-Free Recursive Sequences?

Sep 24, 2005 · Replies 2 · Sep 24, 2005

Replies: 2

Views: 3K

Question on Defining Linear Equation

Sep 20, 2005 · Replies 7 · Sep 23, 2005

Replies: 7

Views: 5K

A formula of prime numbers for interval (q; (q+1)^2)

Sep 21, 2005 · Replies 3 · Sep 21, 2005

Replies: 3

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.

Top