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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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Understanding Oblique Projection and its Geometry

Apr 3, 2009 · Replies 3 · Apr 6, 2009

Replies: 3

Views: 8K

Infinite dimensional representation of su(2)

Apr 3, 2009 · Replies 6 · Apr 6, 2009

Replies: 6

Views: 4K

Defining Addition Operator for Algebra of Rotations in d-Dimensions

Apr 3, 2009 · Replies 7 · Apr 5, 2009

Replies: 7

Views: 2K

Sum of Distinct Primes: Fact or Fiction?

Mar 29, 2009 · Replies 5 · Apr 4, 2009

Replies: 5

Views: 5K

Finding Solutions for na=0 (mod m) with Positive Integers m and n

Apr 2, 2009 · Replies 4 · Apr 3, 2009

Replies: 4

Views: 3K

Is the Riemann Hypothesis Finally Proven?

Apr 2, 2009 · Replies 4 · Apr 2, 2009

Replies: 4

Views: 3K

Is u Algebraic Over K if u^2 is Algebraic Over F?

Apr 2, 2009 · Replies 2 · Apr 2, 2009

Replies: 2

Views: 2K

Invertible <=> F is 1-1 and onto

Apr 2, 2009 · Replies 1 · Apr 2, 2009

Replies: 1

Views: 2K

What are the conditions for commuting linear maps?

Apr 2, 2009 · Replies 4 · Apr 2, 2009

Replies: 4

Views: 4K

Linear transformation defined by T(a + bx) = (a, a+b)

Apr 1, 2009 · Replies 2 · Apr 1, 2009

Replies: 2

Views: 2K

Proving If Two Integers Don't Divide by 3: A Number Theory Challenge

Mar 26, 2009 · Replies 5 · Apr 1, 2009

Replies: 5

Views: 3K

GR Math: how does tensor linearity work?

Mar 23, 2009 · Replies 7 · Apr 1, 2009

Replies: 7

Views: 3K

Lorentz according to Bamberg & Sternberg

Apr 1, 2009 · Replies 3 · Apr 1, 2009

Replies: 3

Views: 3K

Understanding Singular Rectangular Matrices

Apr 1, 2009 · Replies 1 · Apr 1, 2009

Replies: 1

Views: 2K

Need books/articles with proofs of polygonal number theorem

Mar 31, 2009 · Replies 1 · Mar 31, 2009

Replies: 1

Views: 3K

Composition of Linear Transformation and Matrix Multiplication

Mar 30, 2009 · Replies 2 · Mar 31, 2009

Replies: 2

Views: 3K

Is Matrix C Singular If Matrix B Is Singular?

Sep 22, 2004 · Replies 7 · Mar 30, 2009

Replies: 7

Views: 10K

What Does a Strong Eigenvalue Signify in a System of Equations?

Mar 27, 2009 · Replies 3 · Mar 29, 2009

Replies: 3

Views: 6K

Proving the Inverse Element in Modulo Multiplication?

Mar 27, 2009 · Replies 7 · Mar 29, 2009

Replies: 7

Views: 6K

Morphism which preserves convolution?

Mar 27, 2009 · Replies 3 · Mar 29, 2009

Replies: 3

Views: 2K

Is There a Geometrical Interpretation of Vector Pointwise-Product?

Mar 8, 2009 · Replies 21 · Mar 28, 2009

Replies: 21

Views: 13K

Antisymmetric but non-symplectic

Mar 27, 2009 · Replies 2 · Mar 28, 2009

Replies: 2

Views: 2K

Integer tuples with equal L1 and L2 norms

Mar 27, 2009 · Replies 1 · Mar 27, 2009

Replies: 1

Views: 3K

Solving Quadratic Form Derivative: A Frustrating Challenge

Mar 24, 2009 · Replies 4 · Mar 27, 2009

Replies: 4

Views: 3K

Finding the Number of Cubes in the Middle of a Decreasing Cube Tower

Mar 26, 2009 · Replies 4 · Mar 26, 2009

Replies: 4

Views: 6K

Exploring Beal Conjecture Solutions: Common Prime Factor Examples

Aug 29, 2005 · Replies 1 · Mar 26, 2009

Replies: 1

Views: 4K

Some linear algebra problems i with

Mar 24, 2009 · Replies 6 · Mar 25, 2009

Replies: 6

Views: 15K

Understanding LA: Linear Transformation of Matrix A

Mar 25, 2009 · Replies 3 · Mar 25, 2009

Replies: 3

Views: 2K

Do Integral Properties of Functions Imply Independence from Variables?

Mar 25, 2009 · Replies 3 · Mar 25, 2009

Replies: 3

Views: 2K

What is Spanning and its Relation to Dimensionality?

Mar 16, 2009 · Replies 9 · Mar 25, 2009

Replies: 9

Views: 3K

An Elementary Proof Of Both The Beal Conjecture And Fermat's Last Theorem.

Mar 20, 2009 · Replies 38 · Mar 25, 2009

2

Replies: 38

Views: 14K

A question of order of the product of two elements

Mar 25, 2009 · Replies 1 · Mar 25, 2009

Replies: 1

Views: 2K

Is there a theorem for expanding (a^n)-1?

Mar 25, 2009 · Replies 1 · Mar 25, 2009

Replies: 1

Views: 2K

What fields of number theory do I need to learn to understand Wiles' proof?

Mar 22, 2009 · Replies 5 · Mar 25, 2009

Replies: 5

Views: 4K

Why Can't a Module Have Finite & Infinite Basis?

Mar 24, 2009 · Replies 2 · Mar 24, 2009

Replies: 2

Views: 2K

Bases, Invertibility and Injectivity Query

Mar 24, 2009 · Replies 2 · Mar 24, 2009

Replies: 2

Views: 2K

Can we reach all the irrationals?

Mar 23, 2009 · Replies 6 · Mar 24, 2009

Replies: 6

Views: 3K

Transforming a 6x6 stiffness matrix

Mar 23, 2009 · Replies 1 · Mar 23, 2009

Replies: 1

Views: 11K

Strang's book, question about exercise

Mar 23, 2009 · Replies 1 · Mar 23, 2009

Replies: 1

Views: 2K

What is the derivation of the character formula for SU(2) representation?

Mar 23, 2009 · Replies 3 · Mar 23, 2009

Replies: 3

Views: 3K

For vector AB, how to find vector B given vector A and the angle between

Mar 21, 2009 · Replies 5 · Mar 23, 2009

Replies: 5

Views: 21K

What do the directions of eigenvalues represent?

Mar 7, 2009 · Replies 3 · Mar 19, 2009

Replies: 3

Views: 7K

Composition of Linear Transformation and Matrix Multiplication2

Mar 18, 2009 · Replies 1 · Mar 19, 2009

Replies: 1

Views: 2K

Topological properties on Linear spaces

Mar 18, 2009 · Replies 3 · Mar 18, 2009

Replies: 3

Views: 2K

Can Vector Spaces be Considered Spans?

Mar 17, 2009 · Replies 4 · Mar 17, 2009

Replies: 4

Views: 2K

Reasons why infinity hasn't been implemented into modern math

Jul 5, 2008 · Replies 66 · Mar 17, 2009

3

Replies: 66

Views: 14K

Do Algebra Representations Impact Theoretical Physics and Pure Mathematics?

Mar 15, 2009 · Replies 12 · Mar 16, 2009

Replies: 12

Views: 3K

A nonlinear system of algebraic equations

Mar 16, 2009 · Replies 1 · Mar 16, 2009

Replies: 1

Views: 3K

Finite abelian group of size p-1

Mar 14, 2009 · Replies 6 · Mar 16, 2009

Replies: 6

Views: 4K

How do I convert a parametric equation to cartesian form for calculus analysis?

Mar 16, 2009 · Replies 1 · Mar 16, 2009

Replies: 1

Views: 2K

Are Elements of Z/60 Invertible Based on GCD with 60?

Mar 15, 2009 · Replies 1 · Mar 15, 2009

Replies: 1

Views: 3K

Computer Vision, Corners and Eigenvalues

Mar 13, 2009 · Replies 3 · Mar 15, 2009

Replies: 3

Views: 4K

Order of 3 modulo a Mersenne prime

Mar 7, 2009 · Replies 4 · Mar 15, 2009

Replies: 4

Views: 4K

Is the Tensor Product of SU(2) Representations Reducible?

Mar 11, 2009 · Replies 14 · Mar 14, 2009

Replies: 14

Views: 3K

Various proofs I just want to verify

Mar 14, 2009 · Replies 6 · Mar 14, 2009

Replies: 6

Views: 2K

Coordinate Transformation - velocity?

Mar 12, 2009 · Replies 2 · Mar 14, 2009

Replies: 2

Views: 11K

Solving the Prime Numbers Problem: Proving p=q with p and q as Prime Numbers

Mar 10, 2009 · Replies 10 · Mar 13, 2009

Replies: 10

Views: 3K

Map vector A onto line l would that mean the projection of A

Mar 13, 2009 · Replies 2 · Mar 13, 2009

Replies: 2

Views: 2K

Quartic with complex coefficients

Mar 12, 2009 · Replies 2 · Mar 13, 2009

Replies: 2

Views: 3K

Surjective Function: A to B Mapping

Mar 11, 2009 · Replies 1 · Mar 12, 2009

Replies: 1

Views: 2K

Math Physics: Kronecker Delta Fn in Cylindrical/Spherical Polar Coords

Mar 12, 2009 · Replies 1 · Mar 12, 2009

Replies: 1

Views: 2K

On proving real vector spaces (subspaces)

Jan 31, 2004 · Replies 6 · Mar 12, 2009

Replies: 6

Views: 6K

Surjective Function: A to B Mapping

Mar 11, 2009 · Replies 3 · Mar 12, 2009

Replies: 3

Views: 3K

Nilpotency of Matrix with one eigenvalue

Mar 11, 2009 · Replies 2 · Mar 11, 2009

Replies: 2

Views: 2K

Invertible Matrix A & B: True Formulas

Mar 11, 2009 · Replies 2 · Mar 11, 2009

Replies: 2

Views: 2K

Can You Find Matrices B and C Where AB = AC but B ≠ C?

Mar 10, 2009 · Replies 1 · Mar 11, 2009

Replies: 1

Views: 2K

Whether the morphism has special name

Mar 10, 2009 · Replies 1 · Mar 10, 2009

Replies: 1

Views: 2K

What is the minimal subgroup that contains two arbitrary subgroups?

Mar 7, 2009 · Replies 12 · Mar 10, 2009

Replies: 12

Views: 3K

Some help with a continued fraction?

Mar 9, 2009 · Replies 3 · Mar 10, 2009

Replies: 3

Views: 3K

Factors of product of n distinct primes

Mar 9, 2009 · Replies 7 · Mar 10, 2009

Replies: 7

Views: 5K

Why is the formal derivative of a polynomial important in algebra?

Mar 6, 2009 · Replies 16 · Mar 10, 2009

Replies: 16

Views: 3K

Exercise 56 in chapter 1 of Lang's algebra

Mar 9, 2009 · Replies 1 · Mar 9, 2009

Replies: 1

Views: 3K

I still don't quite get the idea of subspaces, span, and range

Feb 25, 2009 · Replies 8 · Mar 8, 2009

Replies: 8

Views: 23K

Inverse (LS) problem for binary data

Mar 4, 2009 · Replies 8 · Mar 8, 2009

Replies: 8

Views: 3K

Union of subspaces of a linear space

Mar 7, 2009 · Replies 11 · Mar 7, 2009

Replies: 11

Views: 4K

Determine whether or not something is a subspace

Mar 7, 2009 · Replies 3 · Mar 7, 2009

Replies: 3

Views: 23K

Proving Normality of [G,G] in G: A Commutator Question

Mar 7, 2009 · Replies 2 · Mar 7, 2009

Replies: 2

Views: 2K

Most Unreliable Technique in the World to compute pi

Mar 6, 2009 · Replies 4 · Mar 6, 2009

Replies: 4

Views: 4K

How can I convert this grammar into a normal form?

Mar 5, 2009 · Replies 1 · Mar 6, 2009

Replies: 1

Views: 2K

Linerization of non-linear models

Mar 6, 2009 · Replies 1 · Mar 6, 2009

Replies: 1

Views: 2K

Is There a Specific Name for This Endomorphism or Subset?

Mar 4, 2009 · Replies 12 · Mar 6, 2009

Replies: 12

Views: 3K

A simple question about isomorphisms

Feb 25, 2009 · Replies 11 · Mar 4, 2009

Replies: 11

Views: 3K

Are prime numbers truly unpredictable?

Mar 2, 2009 · Replies 20 · Mar 4, 2009

Replies: 20

Views: 5K

Are these statements TRUE or FALSE and why?

Mar 3, 2009 · Replies 3 · Mar 4, 2009

Replies: 3

Views: 4K

Proving Injectivity and the Identity Map for Finite Dimensional Linear Maps

Feb 25, 2008 · Replies 12 · Mar 4, 2009

Replies: 12

Views: 8K

How Can Subgroups Be Defined in Universal Algebra?

Mar 3, 2009 · Replies 1 · Mar 3, 2009

Replies: 1

Views: 2K

Analysis of A-Module Endomorphism \phi: Understanding Kronecker Delta Function

Feb 27, 2009 · Replies 1 · Mar 3, 2009

Replies: 1

Views: 2K

Linear Algebra: Finding the Inverse of a Matrix

Mar 2, 2009 · Replies 2 · Mar 3, 2009

Replies: 2

Views: 2K

How to formalize this unary operation?

Mar 2, 2009 · Replies 3 · Mar 3, 2009

Replies: 3

Views: 2K

What is the meaning of det V and det V* in Generalised Complex geometry?

Mar 2, 2009 · Replies 1 · Mar 2, 2009

Replies: 1

Views: 4K

Linear algebra question about matrices

Mar 1, 2009 · Replies 6 · Mar 2, 2009

Replies: 6

Views: 3K

What Is the Order of \(a*b\) Given the Orders of \(a\) and \(b\)?

Feb 28, 2009 · Replies 2 · Mar 1, 2009

Replies: 2

Views: 4K

Can a Function be Composed with Itself to Solve a Differential Equation?

Feb 27, 2009 · Replies 8 · Mar 1, 2009

Replies: 8

Views: 3K

Are Binomial Coefficients and Fibonacci Numbers Related?

Feb 24, 2009 · Replies 4 · Feb 28, 2009

Replies: 4

Views: 3K

What do we call the function in this diagram?

Feb 28, 2009 · Replies 1 · Feb 28, 2009

Replies: 1

Views: 2K

Silly question, could use some assistance

Feb 27, 2009 · Replies 6 · Feb 27, 2009

Replies: 6

Views: 2K

Algorithmic Complexity and Big-Oh notation

Dec 20, 2008 · Replies 6 · Feb 27, 2009

Replies: 6

Views: 15K

What is the subspace spanned by a single vector in function space?

Feb 27, 2009 · Replies 1 · Feb 27, 2009

Replies: 1

Views: 3K

How Many Involutions Can Be Defined in the Set of Real Functions?

Feb 27, 2009 · Replies 2 · Feb 27, 2009

Replies: 2

Views: 8K

Can Cosine Affect Whether Three Nonzero Vectors Must Lie in the Same Plane?

Feb 25, 2009 · Replies 2 · Feb 27, 2009

Replies: 2

Views: 4K

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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