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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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Product of a specific sequence of prime number squares

Dec 26, 2011 · Replies 2 · Jan 15, 2012

Replies: 2

Views: 3K

Solving Matrix equstions of the type: AX = C (FIND The X) - (NOT HW)

Jan 13, 2012 · Replies 3 · Jan 14, 2012

Replies: 3

Views: 5K

Algebra-Modules generalize Ring-Modules?

Jan 11, 2012 · Replies 2 · Jan 14, 2012

Replies: 2

Views: 3K

What Does a = b (mod pZp) Mean in p-adic Numbers?

Jan 11, 2012 · Replies 4 · Jan 13, 2012

Replies: 4

Views: 3K

Question regarding quadratic-like residues in (Z/pZ) .

Jan 13, 2012 · Replies 2 · Jan 13, 2012

Replies: 2

Views: 3K

Group like elements of Universal enveloping algebras

Jan 12, 2012 · Replies 1 · Jan 13, 2012

Replies: 1

Views: 2K

Finite Groups and Three Dimensional Pseudo Real Representations: An Exploration

Jan 4, 2012 · Replies 4 · Jan 13, 2012

Replies: 4

Views: 5K

Generating Function: Formula for Nth Term?

Dec 27, 2011 · Replies 6 · Jan 13, 2012

Replies: 6

Views: 4K

Prove that (n) is divisible by (n)^(n-1)

Jan 12, 2012 · Replies 2 · Jan 12, 2012

Replies: 2

Views: 3K

2-norm Pseudoinverse Upper Bound

Jan 8, 2012 · Replies 3 · Jan 12, 2012

Replies: 3

Views: 5K

Qual Problem: When do Matrices Commute?

Jan 11, 2012 · Replies 5 · Jan 11, 2012

Replies: 5

Views: 7K

Efficient Computation of Square Root of Covariance Matrix

Jan 10, 2012 · Replies 2 · Jan 11, 2012

Replies: 2

Views: 4K

Direct product of two groups with different n-spaces

Jan 11, 2012 · Replies 2 · Jan 11, 2012

Replies: 2

Views: 2K

Projecting 3D point to 2D / view-point

Jan 9, 2012 · Replies 4 · Jan 11, 2012

Replies: 4

Views: 6K

Complex / imaginary numbers trigonometric graphs

Jan 10, 2012 · Replies 1 · Jan 11, 2012

Replies: 1

Views: 2K

Efficient Algorithm for Calculating f(x)modg(x) with Large Degrees

Jan 2, 2012 · Replies 1 · Jan 10, 2012

Replies: 1

Views: 3K

Understanding Matrix Solutions: AX=B vs. AX=0

Jan 9, 2012 · Replies 3 · Jan 10, 2012

Replies: 3

Views: 3K

Any numbers being Complex numbers

Jan 9, 2012 · Replies 3 · Jan 9, 2012

Replies: 3

Views: 3K

An approach to the Twin Prime Conjecture

Jan 6, 2012 · Replies 14 · Jan 8, 2012

Replies: 14

Views: 6K

Generalizations of Determinants: Permanents, Immanants, etc.

Dec 30, 2011 · Replies 2 · Jan 7, 2012

Replies: 2

Views: 3K

Proving non-existence of integer solutions by reducing mod p

Jan 4, 2012 · Replies 5 · Jan 6, 2012

Replies: 5

Views: 7K

Modulo division with negative power ?

Jan 5, 2012 · Replies 1 · Jan 5, 2012

Replies: 1

Views: 3K

Permutations commuting with their powers

Dec 1, 2007 · Replies 8 · Jan 5, 2012

Replies: 8

Views: 7K

Transpose of a matrix with mixed indices

Jan 4, 2012 · Replies 4 · Jan 5, 2012

Replies: 4

Views: 4K

What Happens if Coefficients of Kronecker Delta are Zero?

Jan 5, 2012 · Replies 10 · Jan 5, 2012

Replies: 10

Views: 4K

Help with extracting alpha from: -alpha-asin(sin(alpha)(r/l)

Jan 4, 2012 · Replies 3 · Jan 4, 2012

Replies: 3

Views: 3K

Is f(x) = ax + b Truly a Linear Function?

Jan 4, 2012 · Replies 1 · Jan 4, 2012

Replies: 1

Views: 2K

Solving Equation Ʃ(ai^x -b)^2 = C

Dec 28, 2011 · Replies 7 · Jan 4, 2012

Replies: 7

Views: 3K

What is the difference between roots and weights in Lie algebra theory?

Dec 22, 2011 · Replies 1 · Jan 4, 2012

Replies: 1

Views: 3K

Help proving equality of matrix expressions

Jan 3, 2012 · Replies 3 · Jan 4, 2012

Replies: 3

Views: 3K

Resetting the Affine Transformation matrix

Jan 3, 2012 · Replies 2 · Jan 3, 2012

Replies: 2

Views: 3K

GEBRA: Representation and Operations of Matrices - FAQs

Jan 3, 2012 · Replies 2 · Jan 3, 2012

Replies: 2

Views: 3K

What is the frustration with a professor's teaching style?

Dec 28, 2011 · Replies 7 · Jan 2, 2012

Replies: 7

Views: 3K

What does eigenvalues and eigenvectors mean?

Jan 1, 2012 · Replies 2 · Jan 2, 2012

Replies: 2

Views: 11K

Complex solution of a cubic function.

Dec 31, 2011 · Replies 2 · Jan 2, 2012

Replies: 2

Views: 3K

Further Maths, D1 - Dijkstra's Algorithm

Oct 28, 2011 · Replies 4 · Jan 2, 2012

Replies: 4

Views: 6K

Help with Mobius Inversion in Riemann's Zeta Function by Edwards (J to Prime Pi)

Dec 28, 2011 · Replies 2 · Jan 1, 2012

Replies: 2

Views: 6K

Difference in Powers of Odd Primes

Dec 22, 2011 · Replies 3 · Dec 30, 2011

Replies: 3

Views: 4K

When Is the Mod2-Reduction Map Onto for Matrix Groups?

Aug 2, 2011 · Replies 2 · Dec 30, 2011

Replies: 2

Views: 3K

Injective and Surjective linear transformations

Dec 28, 2011 · Replies 4 · Dec 29, 2011

Replies: 4

Views: 5K

Roots of Cubic Polynomials over R

Dec 28, 2011 · Replies 3 · Dec 28, 2011

Replies: 3

Views: 3K

Can 3-fields be consistently defined and constructed?

Dec 24, 2011 · Replies 8 · Dec 28, 2011

Replies: 8

Views: 4K

Which Homomorphisms are Injective and Surjective between Z plus and Z plus?

Dec 14, 2011 · Replies 2 · Dec 28, 2011

Replies: 2

Views: 4K

Isomorphism & Isometry: Hilbert Spaces

Dec 22, 2011 · Replies 17 · Dec 28, 2011

Replies: 17

Views: 7K

Eigenvalues of a completely disconnected graph

Dec 28, 2011 · Replies 8 · Dec 28, 2011

Replies: 8

Views: 4K

Eigenvalues for a 400x400 normalized laplacian of a graph

Dec 28, 2011 · Replies 8 · Dec 28, 2011

Replies: 8

Views: 3K

Eigenvalues and eigenvectors of symmetric 2x2 matrix?

Jun 11, 2009 · Replies 5 · Dec 28, 2011

Replies: 5

Views: 14K

Why is BEDMAS/PEMDAS a widely used convention in mathematics?

Dec 24, 2011 · Replies 2 · Dec 27, 2011

Replies: 2

Views: 4K

Find the nth Term of a Generating Function

Dec 24, 2011 · Replies 1 · Dec 26, 2011

Replies: 1

Views: 4K

What are some good sources for learning abstract algebra?

Dec 24, 2011 · Replies 1 · Dec 25, 2011

Replies: 1

Views: 3K

Maximal subgroup of a product of groups?

Dec 24, 2011 · Replies 2 · Dec 25, 2011

Replies: 2

Views: 2K

Diagonalizing A: Is it Possible with Rational Numbers?

Dec 23, 2011 · Replies 2 · Dec 24, 2011

Replies: 2

Views: 8K

Generating Function for 0,1 Sequences with Period m

Dec 22, 2011 · Replies 8 · Dec 24, 2011

Replies: 8

Views: 3K

How do change of basis matrices work in linear algebra?

Dec 21, 2011 · Replies 3 · Dec 23, 2011

Replies: 3

Views: 4K

Finding the nth Partial Sum for a Series Involving Floor and Mod Operators

Dec 22, 2011 · Replies 6 · Dec 23, 2011

Replies: 6

Views: 4K

Skyline storage is only for symetric matrices?

Dec 22, 2011 · Replies 1 · Dec 22, 2011

Replies: 1

Views: 3K

Can Euler's Formula Be Modified to Create a Logarithmic Spiral?

Dec 19, 2011 · Replies 13 · Dec 21, 2011

Replies: 13

Views: 5K

How do I numerically find eigenvectors for given eigenvalues?

Dec 20, 2011 · Replies 6 · Dec 21, 2011

Replies: 6

Views: 18K

Question about the permutations of roots as polynomial coefficients

Dec 20, 2011 · Replies 2 · Dec 20, 2011

Replies: 2

Views: 3K

Inner Product for Vectors in Complex Space

Oct 18, 2006 · Replies 10 · Dec 20, 2011

Replies: 10

Views: 21K

Question about determinants and characteristic polynomials.

Dec 17, 2011 · Replies 7 · Dec 19, 2011

Replies: 7

Views: 5K

How Can Binary Vectors Be Ordered Through Transformation?

Dec 19, 2011 · Replies 3 · Dec 19, 2011

Replies: 3

Views: 4K

Gauss Composition? and a naive composition law

Dec 13, 2011 · Replies 3 · Dec 19, 2011

Replies: 3

Views: 7K

Solving Queries on Operators: Af = Mf & BAf = f?

Nov 5, 2011 · Replies 9 · Dec 19, 2011

Replies: 9

Views: 3K

Can Eigenvectors Diagonalize a Matrix with Only One Eigenvalue?

Dec 14, 2011 · Replies 1 · Dec 18, 2011

Replies: 1

Views: 3K

Are units considered irreducible

Dec 15, 2011 · Replies 2 · Dec 18, 2011

Replies: 2

Views: 3K

How can we proof this matrix norm equality?

Dec 18, 2011 · Replies 1 · Dec 18, 2011

Replies: 1

Views: 4K

How to determine an infinitely dimensional matrix is positive definite

Dec 15, 2011 · Replies 2 · Dec 18, 2011

Replies: 2

Views: 4K

Linear Programming - Separation of points

Dec 11, 2011 · Replies 7 · Dec 17, 2011

Replies: 7

Views: 6K

What is Nonunique Factorization Theory in Number Theory?

Dec 13, 2011 · Replies 5 · Dec 16, 2011

Replies: 5

Views: 4K

How do stabilizers and isomorphisms work in the Sn group?

Dec 15, 2011 · Replies 1 · Dec 16, 2011

Replies: 1

Views: 3K

Is it possible to extract the diagonal elements of a matrix into a vector?

Dec 15, 2011 · Replies 1 · Dec 15, 2011

Replies: 1

Views: 9K

Fibonacci numbers as coefficients in three variable system of equations

Dec 14, 2011 · Replies 2 · Dec 15, 2011

Replies: 2

Views: 3K

Group isomorphisms and bijective maps

Dec 15, 2011 · Replies 7 · Dec 15, 2011

Replies: 7

Views: 4K

Can a Formula Create True Randomness?

Dec 14, 2011 · Replies 1 · Dec 14, 2011

Replies: 1

Views: 3K

Order of Elements: Non-Abelian Group G & Correlation between |a|, |b|, |ab|?

Dec 10, 2011 · Replies 4 · Dec 14, 2011

Replies: 4

Views: 3K

Components of the trace operation

Dec 13, 2011 · Replies 5 · Dec 13, 2011

Replies: 5

Views: 3K

Need program for operating on 200-digited numbers

Dec 12, 2011 · Replies 5 · Dec 13, 2011

Replies: 5

Views: 4K

Generalized eigenvectors/eigenvalues

Dec 12, 2011 · Replies 5 · Dec 13, 2011

Replies: 5

Views: 6K

Whats the best software to calculate very large numbers?

Dec 3, 2011 · Replies 12 · Dec 13, 2011

Replies: 12

Views: 11K

Subgroups of dihedral group and determining if normal

Dec 7, 2011 · Replies 19 · Dec 12, 2011

Replies: 19

Views: 10K

Evaluating the Accuracy of (Attached) Statements

Dec 11, 2011 · Replies 2 · Dec 12, 2011

Replies: 2

Views: 3K

Is a Subgroup of a Normal Subgroup Always Normal?

Dec 9, 2011 · Replies 15 · Dec 12, 2011

Replies: 15

Views: 4K

Solving z^6 = 1 using De Moivre's Theorem |z|^6(cos 6θ + isin6θ) = 1

Oct 27, 2011 · Replies 9 · Dec 12, 2011

Replies: 9

Views: 5K

Is n(0) Always Equal to 0? A Debate on Friend's Creative Proof

Dec 10, 2011 · Replies 38 · Dec 11, 2011

2

Replies: 38

Views: 10K

Why the inner product of two orthogonal vectors is zero

Dec 11, 2011 · Replies 3 · Dec 11, 2011

Replies: 3

Views: 3K

Rank(AB) = Rank(A)Rank(B)?The Rank Product Theorem for Matrices

Dec 7, 2011 · Replies 1 · Dec 11, 2011

Replies: 1

Views: 3K

Why Must Free Variables Be Non-Leading in Linear Systems?

Dec 9, 2011 · Replies 2 · Dec 11, 2011

Replies: 2

Views: 5K

Why is a Linear Transformation a Type-(1,1) Tensor?

Dec 10, 2011 · Replies 6 · Dec 10, 2011

Replies: 6

Views: 8K

Proving the Simplicity of a Group of Order 36 Using Sylow Subgroups

Dec 7, 2011 · Replies 9 · Dec 10, 2011

Replies: 9

Views: 8K

Let G = D12, given by generators a,b with |a|=6, |b|=2, and ba=a-1b.

Dec 9, 2011 · Replies 2 · Dec 10, 2011

Replies: 2

Views: 2K

General function that represents a series of 1 and 0

Nov 4, 2011 · Replies 28 · Dec 10, 2011

Replies: 28

Views: 7K

A Unitary Matrix and Hermitian Matrix

Dec 9, 2011 · Replies 2 · Dec 10, 2011

Replies: 2

Views: 4K

What is the difference between these two operations?

Dec 9, 2011 · Replies 1 · Dec 9, 2011

Replies: 1

Views: 2K

Multiplicative closure for subring test?

Dec 7, 2011 · Replies 6 · Dec 9, 2011

Replies: 6

Views: 3K

Quaternion Polynomial Equation

Dec 9, 2011 · Replies 3 · Dec 9, 2011

Replies: 3

Views: 4K

Are Intersections of Sylow p-Groups Always Trivial?

Dec 7, 2011 · Replies 4 · Dec 8, 2011

Replies: 4

Views: 7K

How to Find and Prove All Distinct Ideals of a Ring?

Dec 8, 2011 · Replies 1 · Dec 8, 2011

Replies: 1

Views: 3K

Difference among types of bases.

Dec 7, 2011 · Replies 3 · Dec 8, 2011

Replies: 3

Views: 2K

Why is G abelian if |G/Z(G)|=p with p prime?

Dec 2, 2011 · Replies 11 · Dec 8, 2011

Replies: 11

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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