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

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

Replies: 4

Views: 4K

Undergrad Linear Transformation of s u + r V

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

Replies: 2

Views: 4K

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

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

Replies: 6

Views: 6K

Graduate Belian group A that is the direct sum of cyclic groups

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

Replies: 2

Views: 3K

Graduate Necessary and sufficient condition

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

Replies: 4

Views: 4K

Undergrad Trouble understanding how to formulate rhis problem

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

Replies: 3

Views: 2K

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

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

Replies: 6

Views: 3K

Undergrad Finding vector perpendicular to plane

May 9, 2004 · Replies 6 · May 9, 2004

Replies: 6

Views: 46K

Undergrad Sufficiency of n eqs. for n unkwns.

May 7, 2004 · Replies 4 · May 9, 2004

Replies: 4

Views: 2K

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

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

Replies: 10

Views: 3K

Graduate Some theorems regarding decimal representations

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

Replies: 2

Views: 3K

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

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

Replies: 2

Views: 3K

Undergrad General Solutions for three-point parabola

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

Replies: 2

Views: 7K

Graduate 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

Undergrad Some theorem regarding rational numbers

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

Replies: 6

Views: 5K

Graduate What are the ideals in various rings?

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

Replies: 6

Views: 5K

Undergrad Finding the Line of Intersection for Two Planes

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

Replies: 2

Views: 14K

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

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

Replies: 3

Views: 3K

Undergrad Reviewing Algebra for CAT6 Test: 3 Challenging Problems

Apr 25, 2004 · Replies 3 · Apr 25, 2004

Replies: 3

Views: 2K

Undergrad The Bilinear Form Kernel in Mathematics

Apr 21, 2004 · Replies 21 · Apr 24, 2004

Replies: 21

Views: 4K

High School Solving Linear Systems: Verify Your Solution

Apr 21, 2004 · Replies 9 · Apr 24, 2004

Replies: 9

Views: 3K

Undergrad Relationship between Linear Algebra and Differential equations

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

Replies: 3

Views: 9K

Undergrad Matrix M Formulation for Xn and Xn+1

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

Replies: 3

Views: 3K

Graduate Def.: Continuously Indexed Vector Basis?

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

Replies: 6

Views: 3K

High School Solve the system. (1) 5x + 2y = 5 (2) 3x - 4y = -23

Apr 22, 2004 · Replies 1 · Apr 22, 2004

Replies: 1

Views: 2K

Undergrad How to solve an exponential ciphers?

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

Replies: 3

Views: 7K

Graduate How Do Units Determine Norm Values in Rings?

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

Replies: 2

Views: 5K

High School How to Solve for Integers Modulo n?

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

Replies: 4

Views: 4K

High School Why is 10 the Standard Base Number in Mathematics?

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

Replies: 15

Views: 4K

Graduate Understanding Group Orders: A Take Home Problem

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

Replies: 4

Views: 6K

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

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

Replies: 29

Views: 6K

Undergrad Prove any three vectors of R^3 are linear independent

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

Replies: 8

Views: 4K

Graduate Is 1 considered a prime number in a UFD?

Apr 17, 2004 · Replies 10 · Apr 18, 2004

Replies: 10

Views: 4K

Undergrad Homogeneous Equation (easier question)

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

Replies: 2

Views: 6K

Undergrad Equivalance Relations Could some one check my work please?

Apr 13, 2004 · Replies 7 · Apr 15, 2004

Replies: 7

Views: 3K

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

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

Replies: 3

Views: 3K

High School Find the area of the original parallelogram

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

Replies: 2

Views: 3K

Undergrad Sums of digits of Perfect Squares

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

Replies: 25

Views: 21K

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

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

Replies: 2

Views: 3K

Undergrad Guassian elimination and Inverse Matrix

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

Replies: 3

Views: 7K

Undergrad Geometric App's of Linear Algebra

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

Replies: 10

Views: 3K

High School What Is the Term for Decomposing Numbers into Additive Combinations?

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

Replies: 2

Views: 5K

Undergrad Group Theory Basics: Where Can I Learn More?

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

8

Replies: 210

Views: 60K

High School Finding a Book on Basic Number Theory

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

Replies: 2

Views: 4K

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

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

Replies: 15

Views: 3K

Graduate Conjugacy in A_n: Rules & Resources

Apr 4, 2004 · Replies 9 · Apr 5, 2004

Replies: 9

Views: 5K

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

Apr 4, 2004 · Replies 4 · Apr 5, 2004

Replies: 4

Views: 11K

Undergrad Solving Polynomial: p(x) = x^6 + x^4 + x^2 + 1 | Factorization

Apr 1, 2004 · Replies 19 · Apr 3, 2004

Replies: 19

Views: 3K

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

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

Replies: 4

Views: 34K

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

Apr 2, 2004 · Replies 3 · Apr 2, 2004

Replies: 3

Views: 3K

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

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

Replies: 3

Views: 4K

Undergrad Square matrices, determinants and consistency

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

Replies: 2

Views: 19K

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

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

Replies: 5

Views: 12K

Graduate Anyone familiar with Peano' (or Grassman) algebra?

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

Replies: 5

Views: 4K

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

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

Replies: 5

Views: 3K

High School Solve the Mystery: What is 9 times 7?

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

Replies: 3

Views: 3K

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

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

Replies: 3

Views: 16K

Graduate 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

Undergrad Calculating Value of Continued Fraction

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

Replies: 4

Views: 8K

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

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

Replies: 2

Views: 3K

Undergrad What Defines an Equivalence Relation?

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

Replies: 27

Views: 9K

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

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

Replies: 6

Views: 3K

Graduate Geometric Progression of Prime Numbers

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

Replies: 11

Views: 6K

Graduate 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

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

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

Replies: 5

Views: 14K

High School Solving the Puzzle: Ann and Mary's Ages

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

Replies: 2

Views: 3K

High School What is the Largest Integer Factored into Two Primes?

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

Replies: 5

Views: 3K

Graduate Singular Matrices: Disadvantages, Practical Use & Mass Quantization

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

Replies: 12

Views: 5K

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

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

Replies: 2

Views: 4K

Undergrad Man Cashes Cheque: Solve Assumptions to get Amount

Mar 7, 2004 · Replies 2 · Mar 8, 2004

Replies: 2

Views: 3K

High School Understanding x=pmodn: An Integer Modular Arithmetic Primer

Mar 5, 2004 · Replies 2 · Mar 6, 2004

Replies: 2

Views: 3K

Graduate Can recursive square roots reveal the secrets of the golden ratio?

Mar 1, 2004 · Replies 12 · Mar 4, 2004

Replies: 12

Views: 9K

Graduate Extended Fermat's last theorem.

Mar 2, 2004 · Replies 7 · Mar 4, 2004

Replies: 7

Views: 4K

Graduate Proof of the formula for the nth derivative of a product

Feb 12, 2004 · Replies 18 · Mar 3, 2004

Replies: 18

Views: 15K

Undergrad How Do I Proceed with Variable Row Reduction?

Feb 24, 2004 · Replies 2 · Mar 2, 2004

Replies: 2

Views: 3K

Graduate A partial solution to the Goldbach Conjecture

Mar 1, 2004 · Replies 7 · Mar 2, 2004

Replies: 7

Views: 6K

High School Can you easily invert 3 by 3 matrices using a simple formula?

Dec 20, 2003 · Replies 9 · Mar 2, 2004

Replies: 9

Views: 6K

Undergrad How Does Two-Digit Counting Work Across Different Number Bases?

Feb 25, 2004 · Replies 8 · Mar 1, 2004

Replies: 8

Views: 11K

Undergrad Discovering Primes: The Relationship Between p and 2p + 2

Feb 25, 2004 · Replies 18 · Feb 29, 2004

Replies: 18

Views: 4K

Undergrad How to find the matrix for reflecting a triangle over a line in linear algebra?

Feb 25, 2004 · Replies 9 · Feb 29, 2004

Replies: 9

Views: 4K

Undergrad Understanding the Cross Product of Vectors: Perpendicular Properties Explained

Nov 30, 2003 · Replies 42 · Feb 27, 2004

2

Replies: 42

Views: 25K

Graduate Discovering a Simple Inequality for Divisor Count in Positive Integers

Feb 19, 2004 · Replies 2 · Feb 26, 2004

Replies: 2

Views: 3K

Undergrad Using the Euclidean Algorithm to Find Values for x and y in Linear Combinations?

Feb 24, 2004 · Replies 1 · Feb 24, 2004

Replies: 1

Views: 4K

Undergrad Searching for Perfect Squares using the Pythagorean Theorem

Feb 3, 2004 · Replies 2 · Feb 24, 2004

Replies: 2

Views: 3K

Undergrad Understanding Irrational Numbers: Is it Possible to Exact Measure?

Feb 18, 2004 · Replies 4 · Feb 22, 2004

Replies: 4

Views: 4K

High School Solving Simultaneous Equations for Confused Students

Feb 20, 2004 · Replies 9 · Feb 21, 2004

Replies: 9

Views: 3K

Graduate Find a linear differentiation transformation

Feb 18, 2004 · Replies 5 · Feb 20, 2004

Replies: 5

Views: 7K

Undergrad Multiplication=addition 2*2=2+2=4

Feb 12, 2004 · Replies 12 · Feb 19, 2004

Replies: 12

Views: 4K

Graduate Is A invertible if {v1, v2} and {Av1, Av2} are linearly independent sets?

Feb 12, 2004 · Replies 2 · Feb 19, 2004

Replies: 2

Views: 3K

High School Coefficient of Friction: What is the Equation?

Feb 10, 2004 · Replies 2 · Feb 18, 2004

Replies: 2

Views: 3K

Undergrad What are Isomorphisms: A Beginner's Guide to Understanding Algebraic Structures.

Feb 12, 2004 · Replies 10 · Feb 15, 2004

Replies: 10

Views: 7K

Graduate Has the Prime Number Distribution Puzzle Been Cracked?

Sep 29, 2003 · Replies 33 · Feb 14, 2004

2

Replies: 33

Views: 11K

Undergrad Proving Properties of Exponents Using Induction

Feb 10, 2004 · Replies 3 · Feb 11, 2004

Replies: 3

Views: 3K

Undergrad Proving n! > n^2 for n ≥ 4 with Induction

Feb 3, 2004 · Replies 2 · Feb 10, 2004

Replies: 2

Views: 2K

Graduate Clifford Algebra Question on Vectors

Feb 6, 2004 · Replies 5 · Feb 9, 2004

Replies: 5

Views: 3K

Undergrad Solving 4 linear equations with five unknown variables?

Feb 7, 2004 · Replies 4 · Feb 9, 2004

Replies: 4

Views: 2K

Graduate Has Any One solved Fermats Last Theorem ?

Feb 8, 2004 · Replies 6 · Feb 9, 2004

Replies: 6

Views: 5K

Undergrad Vector Spaces and polynomial functions

Feb 7, 2004 · Replies 15 · Feb 8, 2004

Replies: 15

Views: 9K

Undergrad Growth of Functions - What is "Log Star" (O(log*n))?

Feb 7, 2004 · Replies 5 · Feb 7, 2004

Replies: 5

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.

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