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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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High School Why Is (-1)^2 Equal to 1?

Aug 4, 2010 · Replies 19 · Mar 31, 2011

Replies: 19

Views: 6K

Graduate Finding x in Modular Equations with Large Exponents

Mar 31, 2011 · Replies 4 · Mar 31, 2011

Replies: 4

Views: 3K

Graduate Proving Normality in G: An Elegant Approach?

Mar 29, 2011 · Replies 6 · Mar 31, 2011

Replies: 6

Views: 3K

Undergrad I would like to argue about (-8)^(1/3) = -2

Mar 26, 2011 · Replies 10 · Mar 31, 2011

Replies: 10

Views: 4K

Graduate First isomorphism theorem for rings

Mar 30, 2011 · Replies 8 · Mar 31, 2011

Replies: 8

Views: 4K

Graduate Linear Least Squares Minimization

Mar 30, 2011 · Replies 4 · Mar 30, 2011

Replies: 4

Views: 4K

Graduate Prove Summation of Mobius Inversion w/ Sigma Function

Mar 29, 2011 · Replies 5 · Mar 30, 2011

Replies: 5

Views: 3K

Graduate What Is the \|f\|_{C^{1}} Norm?

Mar 29, 2011 · Replies 2 · Mar 30, 2011

Replies: 2

Views: 2K

Graduate Relations bet. Groups, from Relations between Resp. Presentations.

Mar 28, 2011 · Replies 1 · Mar 30, 2011

Replies: 1

Views: 2K

Graduate Solution to x^k=b mod m Using Prime Factors and Mod Congruence

Mar 30, 2011 · Replies 1 · Mar 30, 2011

Replies: 1

Views: 3K

Graduate Good websites for help in Algebra

Mar 29, 2011 · Replies 7 · Mar 30, 2011

Replies: 7

Views: 5K

Undergrad Are Vectors in the Column Space and Nullspace of Matrix A Linearly Independent?

Mar 27, 2011 · Replies 6 · Mar 29, 2011

Replies: 6

Views: 2K

Graduate What is the Concise Proof for the Determinant Product Rule?

Mar 28, 2011 · Replies 8 · Mar 29, 2011

Replies: 8

Views: 8K

Undergrad Does G\H Form a Subgroup of G?

Mar 27, 2011 · Replies 3 · Mar 29, 2011

Replies: 3

Views: 3K

Graduate Why Does the Matrix Transformation Not Equal dxdydz?

Mar 28, 2011 · Replies 2 · Mar 28, 2011

Replies: 2

Views: 2K

Graduate Some thought about direct sum and

Mar 28, 2011 · Replies 2 · Mar 28, 2011

Replies: 2

Views: 2K

Graduate Algorithm to solve a maximization problem

Mar 27, 2011 · Replies 5 · Mar 28, 2011

Replies: 5

Views: 2K

Music of the Primes: Maths Through Musical Patterns

Mar 22, 2011 · Replies 3 · Mar 28, 2011

Replies: 3

Views: 2K

Graduate Fast Construction of Irreducible Polynomials of degree n over any Finite Field

Mar 27, 2011 · Replies 1 · Mar 27, 2011

Replies: 1

Views: 2K

Graduate Fast Construction of Irreducible Polynomials of degree n over any Finite Field

Mar 27, 2011 · Replies 1 · Mar 27, 2011

Replies: 1

Views: 2K

Graduate Are Weight 12 Modular Forms the Only Ones Without Zeros on the Upper Half Plane?

Mar 25, 2011 · Replies 4 · Mar 27, 2011

Replies: 4

Views: 3K

Undergrad Prove that if ab=ac, then b=c.

Mar 26, 2011 · Replies 9 · Mar 27, 2011

Replies: 9

Views: 38K

Graduate Constructing Associated Sheaf of Abelian Groups

Mar 26, 2011 · Replies 2 · Mar 27, 2011

Replies: 2

Views: 2K

Undergrad Rank of a Matrix: Why is A = 1 & Not 0?

Mar 25, 2011 · Replies 5 · Mar 27, 2011

Replies: 5

Views: 22K

Graduate Conjecture: Prime Divisibility & First Differences of Stirling & Eulerian Triangles

Mar 20, 2011 · Replies 1 · Mar 26, 2011

Replies: 1

Views: 3K

Undergrad Scalars and Vectors: The Difference

Mar 26, 2011 · Replies 1 · Mar 26, 2011

Replies: 1

Views: 2K

Graduate How Can I Create a Pseudo-Pi Numerical Base System?

Mar 23, 2011 · Replies 2 · Mar 26, 2011

Replies: 2

Views: 3K

Graduate Is f = n^2 a completely multiplicative function?

Mar 24, 2011 · Replies 4 · Mar 25, 2011

Replies: 4

Views: 2K

Graduate How are R^2 and R^4 isomorphic as VS's over Q?

Mar 24, 2011 · Replies 2 · Mar 25, 2011

Replies: 2

Views: 4K

Graduate Can a Matrix A Equalize Vectors u and v in Different Reference Frames?

Mar 24, 2011 · Replies 2 · Mar 25, 2011

Replies: 2

Views: 3K

Graduate How do we prove tangent lines to conics using homogeneous coordinates?

Mar 24, 2011 · Replies 1 · Mar 25, 2011

Replies: 1

Views: 3K

Undergrad What does the superscripted notation in matrix notation mean?

Mar 24, 2011 · Replies 3 · Mar 25, 2011

Replies: 3

Views: 2K

Graduate Question about Cauchy Theorem to Abelians groups

Mar 24, 2011 · Replies 1 · Mar 24, 2011

Replies: 1

Views: 2K

Graduate Proving Inverses (Matrix Multiplications)

Mar 22, 2011 · Replies 3 · Mar 23, 2011

Replies: 3

Views: 2K

Undergrad Maximize multiple linear equations under a single constraint

Mar 21, 2011 · Replies 10 · Mar 22, 2011

Replies: 10

Views: 8K

Graduate Law of Ratios? derving a differential Fick Equation

Mar 21, 2011 · Replies 2 · Mar 22, 2011

Replies: 2

Views: 5K

Graduate Is There a Connection Between Sine Waves and Prime Numbers in Music?

Feb 15, 2006 · Replies 13 · Mar 22, 2011

Replies: 13

Views: 8K

Graduate How to find a basis for the space of even functions (with some constraints)

Mar 11, 2011 · Replies 11 · Mar 21, 2011

Replies: 11

Views: 6K

Graduate Quick question about identity elements

Mar 21, 2011 · Replies 2 · Mar 21, 2011

Replies: 2

Views: 2K

Graduate Characteristic Polynomials and Nilpotent Operators

Mar 21, 2011 · Replies 5 · Mar 21, 2011

Replies: 5

Views: 3K

Graduate Help with a tan(arccos(z)) question

Feb 24, 2011 · Replies 8 · Mar 21, 2011

Replies: 8

Views: 7K

Graduate Orthogonal Complement in Inner Product Space: W2^\bot\subseteqW1^\bot

Mar 20, 2011 · Replies 4 · Mar 21, 2011

Replies: 4

Views: 3K

Undergrad Order of 2x2 Matrix [[2 3][3 5]]

Mar 20, 2011 · Replies 1 · Mar 20, 2011

Replies: 1

Views: 2K

Graduate How to show I_n + A is invertible

Mar 6, 2011 · Replies 7 · Mar 20, 2011

Replies: 7

Views: 9K

Graduate What is the Automorphism Group really?

Mar 17, 2011 · Replies 7 · Mar 20, 2011

Replies: 7

Views: 8K

Graduate Iterative methods for solving systems of linear differential equations

Mar 18, 2011 · Replies 5 · Mar 20, 2011

Replies: 5

Views: 6K

Undergrad Can all invertible matrices be diagonalized?

Mar 17, 2011 · Replies 5 · Mar 20, 2011

Replies: 5

Views: 3K

Graduate Is 1 a Congruent Number with Odd Integer Solutions to x^4 - y^4 = u^2?

Mar 20, 2011 · Replies 3 · Mar 20, 2011

Replies: 3

Views: 3K

Graduate Setwise stabilizer of a finite set is a maximal subgroup of Sym(N)

Mar 18, 2011 · Replies 3 · Mar 19, 2011

Replies: 3

Views: 3K

Graduate How Is the Square of the Zeta Function Related to the Divisor Function?

Mar 18, 2011 · Replies 2 · Mar 19, 2011

Replies: 2

Views: 4K

Graduate How to Generate Theorems for an Abstract System like Sudoku?

Mar 18, 2011 · Replies 1 · Mar 18, 2011

Replies: 1

Views: 2K

Undergrad Finding the Smallest n for F(n)=24: A Challenge in Integer Solutions

Mar 17, 2011 · Replies 2 · Mar 18, 2011

Replies: 2

Views: 3K

Undergrad Eigenvectors - why must det(A-λI)=0?

Mar 12, 2011 · Replies 10 · Mar 18, 2011

Replies: 10

Views: 12K

Graduate How do mathematicians think about abstract algebra?

Mar 9, 2011 · Replies 8 · Mar 18, 2011

Replies: 8

Views: 8K

Undergrad Confused about col/rows of matrices

Mar 16, 2011 · Replies 1 · Mar 17, 2011

Replies: 1

Views: 3K

Graduate Ken Ono cracks partition number mystery

Jan 22, 2011 · Replies 12 · Mar 17, 2011

Replies: 12

Views: 14K

Undergrad Understanding Jacobian Matrices - Working Through Examples

Mar 16, 2011 · Replies 4 · Mar 17, 2011

Replies: 4

Views: 6K

High School Easy definition of linear algebra

Mar 15, 2011 · Replies 16 · Mar 17, 2011

Replies: 16

Views: 8K

Graduate Are Ideals of Mn(Z) Commutative?

Mar 12, 2011 · Replies 1 · Mar 16, 2011

Replies: 1

Views: 3K

Graduate Can Non-Diagonalizable Matrices Have Square Roots?

Mar 15, 2011 · Replies 7 · Mar 16, 2011

Replies: 7

Views: 6K

Graduate Adjoint representations and Lie Algebras

Mar 13, 2011 · Replies 1 · Mar 16, 2011

Replies: 1

Views: 2K

Undergrad What Are Sums of Integer Powers Called in Number Theory?

Mar 10, 2011 · Replies 8 · Mar 16, 2011

Replies: 8

Views: 3K

Graduate Prove Cyclic Factor Group of a Cyclic Group is Cyclic

Mar 13, 2011 · Replies 6 · Mar 16, 2011

Replies: 6

Views: 2K

Undergrad Row Reduction: Adding Rows in Matrix

Mar 14, 2011 · Replies 2 · Mar 15, 2011

Replies: 2

Views: 2K

Undergrad Possible Row Reduced Echelon Forms

Mar 14, 2011 · Replies 1 · Mar 15, 2011

Replies: 1

Views: 2K

Undergrad Powers of integers and factorials

Mar 13, 2011 · Replies 9 · Mar 15, 2011

Replies: 9

Views: 9K

Undergrad Solving simultaneous equations

Mar 15, 2011 · Replies 1 · Mar 15, 2011

Replies: 1

Views: 3K

Graduate Question from the proof in euler's forumla

Mar 14, 2011 · Replies 5 · Mar 15, 2011

Replies: 5

Views: 6K

Graduate Where can I find a book on group theory in physics?

Mar 15, 2011 · Replies 1 · Mar 15, 2011

Replies: 1

Views: 2K

Graduate Cardinality of a vector space over an infinite field

Mar 14, 2011 · Replies 4 · Mar 14, 2011

Replies: 4

Views: 4K

Graduate Conjugate transpose/real and imaginary parts

Mar 13, 2011 · Replies 5 · Mar 14, 2011

Replies: 5

Views: 4K

Undergrad Cartesian Coordinates in Linear Algebra and Globality

Mar 13, 2011 · Replies 5 · Mar 14, 2011

Replies: 5

Views: 2K

Graduate Proof that irrational numbers do not exist

Mar 1, 2011 · Replies 36 · Mar 14, 2011

2

Replies: 36

Views: 17K

Undergrad Inverse of a square matrix in C

Mar 11, 2011 · Replies 4 · Mar 14, 2011

Replies: 4

Views: 4K

Undergrad Cryptography - modulo arithmetic

Mar 12, 2011 · Replies 2 · Mar 13, 2011

Replies: 2

Views: 2K

Graduate What is the connection between residues and the distribution of prime numbers?

Nov 1, 2010 · Replies 10 · Mar 13, 2011

Replies: 10

Views: 7K

Undergrad How to find the x,y elements of a 3D vector when origin, direction, z are known

Mar 13, 2011 · Replies 3 · Mar 13, 2011

Replies: 3

Views: 3K

Graduate How Do You Compute Minimal and Characteristic Polynomials in F16 Over F2?

Mar 13, 2011 · Replies 2 · Mar 13, 2011

Replies: 2

Views: 4K

Graduate Non-Normal Subgroups in Simple Groups

Mar 12, 2011 · Replies 4 · Mar 13, 2011

Replies: 4

Views: 3K

Graduate Show that one of these functionals is unbounded

Mar 10, 2011 · Replies 9 · Mar 13, 2011

Replies: 9

Views: 3K

Graduate Solving Ring Theory Question - Centralizer of Division Char(D) ≠ 2

Mar 12, 2011 · Replies 2 · Mar 12, 2011

Replies: 2

Views: 2K

Graduate Is There an Upper Bound on Elementary Tensors in Tensor Products?

Mar 11, 2011 · Replies 3 · Mar 12, 2011

Replies: 3

Views: 3K

Graduate Abstract Algebra Hello Experts: Proving Theorems About Ideals and Radicals

Mar 12, 2011 · Replies 6 · Mar 12, 2011

Replies: 6

Views: 2K

Graduate Understanding Geometric Meaning of Ax≤b

Mar 10, 2011 · Replies 5 · Mar 12, 2011

Replies: 5

Views: 2K

Graduate Finding GCD of x,c,y,z: Fast & Easy

Mar 12, 2011 · Replies 1 · Mar 12, 2011

Replies: 1

Views: 3K

Undergrad What is the Dimension of a 3-D Rotation Matrix?

Mar 10, 2011 · Replies 6 · Mar 11, 2011

Replies: 6

Views: 7K

Undergrad Inverse of a Matrix M as a Product of Elementary Row Operations. Uniqueness?

Mar 11, 2011 · Replies 1 · Mar 11, 2011

Replies: 1

Views: 4K

Undergrad Figuring the Last Digit of x^x^x^x

Mar 10, 2011 · Replies 3 · Mar 11, 2011

Replies: 3

Views: 2K

Undergrad Understanding Matrices: Questions & Answers

Mar 9, 2011 · Replies 8 · Mar 10, 2011

Replies: 8

Views: 3K

Graduate Is an Non-Zero Coefficient in a Polynomial a Zero Divisor in R[x]?

Mar 10, 2011 · Replies 3 · Mar 10, 2011

Replies: 3

Views: 4K

Undergrad I have no knowledge of number theory

Feb 23, 2011 · Replies 6 · Mar 9, 2011

Replies: 6

Views: 3K

Graduate Efficiently Compute the Inverse of a Matrix Using Tricky Techniques

Mar 8, 2011 · Replies 3 · Mar 9, 2011

Replies: 3

Views: 2K

Undergrad Finding the minimum area of a triangle

Mar 7, 2011 · Replies 2 · Mar 9, 2011

Replies: 2

Views: 6K

Undergrad Why are positive definite matrices useful?

Mar 8, 2011 · Replies 2 · Mar 9, 2011

Replies: 2

Views: 9K

Undergrad Introductory Calculus or Basic Linear Algebra

Mar 8, 2011 · Replies 1 · Mar 8, 2011

Replies: 1

Views: 3K

Graduate Exploring the Wedge Product & its Role in Vectors & Orthogonality

Mar 6, 2011 · Replies 10 · Mar 8, 2011

Replies: 10

Views: 10K

Graduate How to find jordan form given rank?

Mar 7, 2011 · Replies 1 · Mar 8, 2011

Replies: 1

Views: 3K

Undergrad Solving a Matrix Problem with Trigonometric Functions

Mar 8, 2011 · Replies 4 · Mar 8, 2011

Replies: 4

Views: 4K

High School Is Mary Part of the Problem or Solution?

Mar 7, 2011 · Replies 1 · Mar 7, 2011

Replies: 1

Views: 2K

Undergrad Measuring Sequence Similarity with Absolute Differences

Mar 7, 2011 · Replies 1 · Mar 7, 2011

Replies: 1

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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