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 Cross Product of Vectors a & b: Why 0?
  • · Replies 15 ·
Replies
15
Views
5K
Graduate Hyperplanes H1 and H2 have dimensions p and q
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Why is a semigroup called a semigroup?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Investigating a Function which Mimics Prime Numbers
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Subgroup of Sym(n) Isomorphic to S_(n-1) Except n=6
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Is There an Isomorphism Between S(X) and S(Y) Given a Bijection Between X and Y?
  • · Replies 28 ·
Replies
28
Views
5K
Graduate Structure constants of su(2) and so(3)
  • · Replies 4 ·
Replies
4
Views
13K
Graduate Conjunction of Sets: x,y in Rm+n vs Vector z in R(m+n)
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Normal Subgroup Equality: Closure of a Group?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Diagonalizing a square matrix with degenerate eigenvalues
  • · Replies 4 ·
Replies
4
Views
13K
Undergrad Matrix multiplication of an nxn matrix is the scaling
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Infinite cyclic groups isomorphic to Z
  • · Replies 9 ·
Replies
9
Views
10K
High School Solve Large Numerical Values Without a Calculator
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Understanding Rotation Matrices for nxn Orders
  • · Replies 9 ·
Replies
9
Views
14K
Graduate Proof of normal matrix criterion
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Vector Spaces over Real and Complex Numbers: A Comparison
  • · Replies 15 ·
Replies
15
Views
3K
Graduate What is the extension of the Unique Factorization Theorem to Gaussian Integers?
  • · Replies 5 ·
Replies
5
Views
9K
Graduate How to evaluate Nonorthogonal basis?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is the Role of Formal Constructions in Algebraic Equivalence Classes?
  • · Replies 5 ·
Replies
5
Views
6K
Graduate Is Michael Artin's Algebra Harder Than Spivak's Manifolds?
  • · Replies 15 ·
Replies
15
Views
29K
Undergrad Drawing Protein Helix with Twists and Curves: How to Proceed?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Is it possible to rotate circles in 3D using coordinates and normals?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Simple question on disproving a group isomorphism
  • · Replies 7 ·
Replies
7
Views
7K
Graduate Proving Group Properties of Finite Sets
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Pauli Matrices and Structure Constants
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What is the significance of the number e?
  • · Replies 13 ·
Replies
13
Views
13K
Undergrad Cross product in matrix determinant form
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Difference between a vector space and a field
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Is Isomorphism of Matrix Groups Always Expressed by Linear Maps?
  • · Replies 16 ·
Replies
16
Views
10K
Graduate Findng a group between two groups
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Understanding Matrices and Vectors: Operations, Significance, and Applications
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Eigenvalues & eigenvectors of N x N matrix?
  • · Replies 8 ·
Replies
8
Views
6K
Graduate Does Cholesky Decomposition Change for Complex Matrices?
  • · Replies 4 ·
Replies
4
Views
8K
Graduate Explaining the Riemann Hypothesis and Other Famous Math Problems
  • · Replies 4 ·
Replies
4
Views
7K
Undergrad Basis of Vector Space V: Subset of B = Basis of U?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Polynomial equations whose coefficients are all matrices (was I shouldnot )
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Quick Question About Tensor Products
  • · Replies 9 ·
Replies
9
Views
3K
High School Where Can I Find Online Lectures for Linear Algebra?
  • · Replies 5 ·
Replies
5
Views
23K
Graduate Fermat Last Theorem: a^n+b^n<c^n
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Prime Number Formulas: Find the Nth Prime
  • · Replies 48 ·
2
Replies
48
Views
14K
Graduate How to Compute Eigenvectors for Large Matrices Efficiently?
  • · Replies 9 ·
Replies
9
Views
13K
Graduate Is the Set of Products of Two Ideals Always an Ideal?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Constructing Proofs in Mathematics: Where do I Begin?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Constructing the Generators of SU(8) Group in String Theory
  • · Replies 3 ·
Replies
3
Views
3K
Graduate How Do We Prove \(\forall n\in\mathbb{N}\;\varphi(n)\mid n\) Is False?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad For lack of a better word, Modifiers.
  • · Replies 16 ·
Replies
16
Views
5K
Undergrad Linearly independent but not orthogonal, how come?
  • · Replies 4 ·
Replies
4
Views
49K
Undergrad Eigenvalues of A: Same Eigenspaces for A^-1, Transpose, A^k
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Can Infinite Sets Still Form Groups Under Closure Conditions?
  • · Replies 29 ·
Replies
29
Views
7K
Undergrad Question regarding multiple steps in linear mapping
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Simple prime/GCD proof question
  • · Replies 2 ·
Replies
2
Views
5K
Graduate How Do You Rotate One Vector to Another and Apply the Same Rotation to a Matrix?
  • · Replies 1 ·
Replies
1
Views
6K
High School Pascal Triangle & Its Applications.
  • · Replies 7 ·
Replies
7
Views
12K
Undergrad Understanding Summation and Latex: A Simple Explanation
  • · Replies 3 ·
Replies
3
Views
4K
  • Poll Poll
Graduate Barry Mazur's current BAMS article
  • · Replies 2 ·
Replies
2
Views
3K
Graduate How to diagonalize NxNxNxN matrix
  • · Replies 4 ·
Replies
4
Views
10K
Graduate Solve Cryptography Exercises: Rabbin & RSA Protocols
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Solving Radicals for A,B,C and D: 2^11-1
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Why not randomness for primes' distribution?
  • · Replies 20 ·
Replies
20
Views
6K
Graduate Can a Finitely Generated Group Contain an Infinitely Generated Subgroup?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Connection between polynomials and groups
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Dimension of eigenspace, multiplicity of zero of char.pol.
  • · Replies 5 ·
Replies
5
Views
11K
Undergrad Having difficulty with an Ax=b problem and understanding it
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Proving a Subgroup of a Solvable Group is Solvable
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Prime factorization of rationals
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Euler's theorem as primality test?
  • · Replies 6 ·
Replies
6
Views
5K
High School Is it possible to multiply by 'undefined'?
  • · Replies 7 ·
Replies
7
Views
18K
Graduate Riemann Hypothesis: Question on Critical Line
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is Tensor Product Uniqueness Dependent on the Choice of Linear Functions?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate What Can We Learn from Finite Presentations of Groups?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate What Does It Mean for a Group to Be Generated by Two Subgroups?
  • · Replies 19 ·
Replies
19
Views
11K
Graduate Transforms that Preserve The Dominant Eigenvector?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Field on R^3 and isomorphism between C and R
  • · Replies 5 ·
Replies
5
Views
4K
High School Ancient Numbers: Expressing Values, Devision & Subtraction
  • · Replies 9 ·
Replies
9
Views
6K
Graduate Eigenvalue kind of nilpotent problem
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Understanding Oiler's Approach to the Zetha Function: A Math Book Review
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Algebraic inequality subject to some specific constraints.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Find the point D such that all the triangles have the same area.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Problem with dot product of vectors
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad What is the significance of the structure of numbers?
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad Proving Let A & B be Square Matrices of n x n & AB = 0n
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Proving the Unsolvable: Lagrange's Theorem and 4 Squares
  • · Replies 4 ·
Replies
4
Views
4K
High School Boolean Algebra: What Audio Engineering Majors at UMiami Need to Know
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Units and prime elements in euclidean rings
  • · Replies 10 ·
Replies
10
Views
7K
Graduate Adjoint Multiplicity: A* x A* = (A^2)*?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Normed space and its double dual
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Why is the trivial ring excluded in the definition of a field?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Recognizing a product of two 3d rotations (matrices)
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Exploring Bertrand's Postulate: Maximal Prime Gaps and Conjectures
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Symbolic Vector Manipulation Software?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate How Can a Cyclic Group Define a Field Using Only Addition?
  • · Replies 8 ·
Replies
8
Views
3K
High School Learn Linear Algebra Before Calculus?
  • · Replies 9 ·
Replies
9
Views
52K
Undergrad Transforming base vectors in Matrix.
  • · Replies 11 ·
Replies
11
Views
6K
Undergrad What is the formula for finding the determinant of a 10x10 matrix?
  • · Replies 13 ·
Replies
13
Views
20K
Graduate Is My Integer Factorization Algorithm Flawed?
  • · Replies 9 ·
Replies
9
Views
7K
Graduate What Is the Tensor Product of Vector Spaces?
  • · Replies 33 ·
2
Replies
33
Views
14K
Graduate Proving the 2:1 Ratio of a Triangle's Medians at the Centroid Using Vectors
  • · Replies 1 ·
Replies
1
Views
19K
Undergrad Casey's thread of annoying Linear Algebra questions
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Verifying a Finite Non-Abelian Group with Set of 2x2 Matrices Modulo p
  • · Replies 7 ·
Replies
7
Views
6K
Undergrad Linear programming bank assets problem
  • · Replies 3 ·
Replies
3
Views
7K