Linear and Abstract Algebra Forum

Post thread
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.
Undergrad Simple factorial and matrix question
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Permutation describing action on G-set
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Cartesian equation of plane using two lines?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad What is the significance of the zero vector in a vector space?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad How Do You Determine the Maximum Order of an Element Modulo n?
  • · Replies 10 ·
Replies
10
Views
8K
Graduate Dimension of a Set of Transformations
  • · Replies 7 ·
Replies
7
Views
3K
MHB Find Center of Groups of Order 8
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Abelian group on the natural numbers (including 0) ?
  • · Replies 12 ·
Replies
12
Views
4K
High School Does the following point lie on plane?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Finding out a equation of a plane that is parallel to a plane
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is There a General Way to Format a Counterexample for Diagonal Matrices?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Sylvester's Criterion for Infinite-dimensional Matrices
  • · Replies 10 ·
Replies
10
Views
5K
Undergrad Linear Transformations and Bases
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Many 3x3 Non-Singular Matrices Exist with Four 1s and Five 0s?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Confusion: computation of class number of K=Q(sqrt(30))
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Understanding the Ideal Class Group of Q(√-17)
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad How to interpret absolute value bars?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Galois Groups of Extensions by Roots of Unity
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Combinatorial Number Theory Problem
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Confused with working out the span of a set of vectors in R^2
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How to know if an infinite system of linear equations has a solution
  • · Replies 1 ·
Replies
1
Views
3K
MHB What is the Complete Set of 2x2 Matrices Satisfying $A^2-4A+3I=0$?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Rational numbers that form a group under addition
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Finding a basis for the following vectors.
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Equal Distances Between N Points in R^n-1+ | Solving System of Equations
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad PA=LU decomposition (w/ Partial Pivoting)
  • · Replies 1 ·
Replies
1
Views
5K
High School Algebraic multiplicity of matrix
  • · Replies 9 ·
Replies
9
Views
11K
Graduate How to make matrix positive definite (when it is not)?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Is the Number of Free Variables Constant in Echelon Form Systems?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad What are Ideals and Polynomial Rings? A Simple Explanation and Concrete Example
  • · Replies 11 ·
Replies
11
Views
5K
Graduate Help Develop Tongue in Cheek Abstract Algebra Proof
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Maximum inner product between two orthgonal vectors (in standard dot procut))
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Show that two polynomials cannot span P2.
  • · Replies 3 ·
Replies
3
Views
6K
Undergrad Group representations, interesting aspects?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Finding the basis for a set of vectors.
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Writing a matrix as sum of a constant * matrix
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Solving Quadratic Diophantine Equations with A=0, C=0
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Linear independence of sin (x), cos (x) and 1, proof
  • · Replies 5 ·
Replies
5
Views
17K
High School Zeroes at the end of a FACTORIAL
  • · Replies 7 ·
Replies
7
Views
27K
Graduate Finite Reflection Groups in Two Dimensions - R2
  • · Replies 4 ·
Replies
4
Views
2K
Graduate So is chike obo proof of fermat's last theorem
  • · Replies 3 ·
Replies
3
Views
6K
Undergrad Proving 2-Norm of A: Understanding the Relationship Between u and v
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Field extension, properties,proof
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Continuous matrix = differential operator?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Are e and π Transcendental Numbers? Investigating the Rationality of e + π
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad How to calculate powers of a 2x2 matrix WITHOUT eigenvectors ?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Proving Jordan Canonical Form for Similarity of Matrices with Same Polynomials
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Computing a kronecker product of two matrices
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Finding Real Solutions for x-tanh ax = 0 with a>1
  • · Replies 16 ·
Replies
16
Views
5K
Graduate Does d dividing n imply phi(d) divides phi(n)?
  • · Replies 11 ·
Replies
11
Views
14K
Undergrad Question on subspaces and spans of vector spaces
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Offset between non-homogeneous and homogeneous recurrence sequences
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Aligning a matrix with its eigen vectors and other questions?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Jordan Normal Form & Generalized Eigenvectors
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Induction Method: My Question About Theorem in Finite Groups
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How to learn to like number theory
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Eigenvalues of the product of two matrices
  • · Replies 24 ·
Replies
24
Views
70K
High School Understanding Vector Products - Mike's Query
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Mertens function : new formulation
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Help me understand a line in an ATA is positive, semi-definite proof
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Matrix Multiplication to translate object with given vertices
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Proving that the parity of a permutation is well defined.
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Factorize x^2 - z*y^2 with Gcd(x,y)=1, Gcd(x,z)=1, Gcd(y,z)=1, and z squarefree
  • · Replies 15 ·
Replies
15
Views
6K
Undergrad Eigenvalues & Eigenvectors: Repeated vs Distinct
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Expressing matrices as outer product of two vectors
  • · Replies 12 ·
Replies
12
Views
16K
Graduate Putting a matrix into Rational Canonical Form
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Matrix Multiplication and Commuting
  • · Replies 12 ·
Replies
12
Views
55K
Graduate Describing Matrix/Transformation by Eigens.
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad How to calculate complex dot products
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Relationship between eigenspace and column space
  • · Replies 3 ·
Replies
3
Views
11K
Undergrad Quick question about groups and their properties
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Algebraic multiplicity of the matrix
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Confusion between orthogonal sum and orthogonal direct sum
  • · Replies 2 ·
Replies
2
Views
10K
Undergrad Relationship between column space of a matrix and rref of matrix
  • · Replies 7 ·
Replies
7
Views
10K
Graduate Lanczos Method: Calculating Smallest Eigenvalues
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Can a nonabelian group of order p^3 be constructed for any prime p?
  • · Replies 9 ·
Replies
9
Views
7K
Undergrad Mathematica Vector Fields Explaination.
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Various Proofs Regarding Divisors and Properties of Divisors
  • · Replies 17 ·
Replies
17
Views
8K
Undergrad Definition questions for linear algebra
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Linear Algebra Proof of Span and orthogonal vector space
  • · Replies 1 ·
Replies
1
Views
3K
MHB Are Units and Principal Ideals Related in Rings?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Maximal number of bases for which composite number is Fermat pseudoprime
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Solving Vector Norm with F Matrix: Advice from Jo
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Meaning of eigenvectors and values of a 2x2 matrix (2nd order tensor)
  • · Replies 3 ·
Replies
3
Views
4K
Graduate How Can the Fibonacci Sequence Be Proved by Induction?
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Can Eigenvalues of Matrix Addition Be Simplified?
  • · Replies 3 ·
Replies
3
Views
13K
Undergrad What Does \Re2 \rightarrow \Re2 Mean in Linear Transformations?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Is f(a) Always 1 or Legendre Symbol?
  • · Replies 10 ·
Replies
10
Views
4K
MHB Solving for Unit Vectors in U Given Vector 1 and Matrix S
  • · Replies 1 ·
Replies
1
Views
3K
Graduate How to prove that pZ is a maximal ideal for the ring of integers?
  • · Replies 25 ·
Replies
25
Views
16K
Graduate Picard-Vessiot Extension over a Differential Field?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving Orthogonal Polynomials: A Weighted Integral
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Where does p = 5 (mod 8) solve x^2 = a?
  • · Replies 5 ·
Replies
5
Views
9K
Graduate A≡b mod n true in ring of algebraic integers => true in ring of integers
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Are these two linear maps equivalent?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Is the Degree of Q(a) Over Q Correctly Understood?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How do you solve equations with matrices?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Diagonalization and similar matrices
  • · Replies 3 ·
Replies
3
Views
3K
Graduate What Maps Belong to Aut(S2)/SO(3)?
  • · Replies 15 ·
Replies
15
Views
4K
Graduate How to prove the field extension is algebraically closed
  • · Replies 8 ·
Replies
8
Views
4K