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 Solving Linear Systems (Basic Question)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What is a vector valued in a function?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How to Calculate π^σ If We Have 2 Disjoint Cycles?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate How to calculate center coordinates of two reverse arcs in 3D space
  • · Replies 3 ·
Replies
3
Views
2K
MHB At Least p+1 p-Subgroups in Finite Group G
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to find unique solution of X
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Misunderstanding a Theorem on Field Homomorphism
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Factoring Algorithms for Exponential Speed | Tips & Advice
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Why are certain transformations in the case of D4 group considered even or odd?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Linear system in polar coordinates
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Factor (Quotient) Space definitions.
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Solutions of a system of linear equations
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Quick definition question: Dihedral group
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Can the inverse of a matrix exponential be proven using its definition?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Why Is a Group with Identical Elements Considered Unfaithful?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Sums of Ideals - R. Y. Sharp "Steps in Commutative Algebra"
  • · Replies 2 ·
Replies
2
Views
2K
MHB Union of Monoids: Is $(G\cup H,\cdot)$ A Monoid?
  • · Replies 14 ·
Replies
14
Views
4K
Graduate An extension of Dot and Cross Product
  • · Replies 10 ·
Replies
10
Views
3K
MHB The Ideal (x1, x2, .... .... xn)^m
  • · Replies 6 ·
Replies
6
Views
2K
Graduate What Are the Utilities of Interior and Exterior Products?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Structure of R[X] and an exercise on ring adjunction
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Stuck on Rank(G/H) = Rank(G) - Rank(H) Should be trivial(?)
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What Symmetry Group Does the Quantum Harmonic Oscillator Exhibit?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Eigenvalues of 2 matrices are equal
  • · Replies 1 ·
Replies
1
Views
2K
MHB Show Self-Adjointness of Operator E on $L_{2}$ of Square Integrable Functions
  • · Replies 4 ·
Replies
4
Views
2K
MHB Products of ideals of K[x1, x2, x3, x4]
  • · Replies 8 ·
Replies
8
Views
2K
MHB Residue Class Rings (Factor Rings) of Polynomials _ R Y Sharp
  • · Replies 4 ·
Replies
4
Views
3K
MHB How Do You Solve Exercises Involving 2D and 3D Vectors and Dot Product?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Face of face of a cone is a face. Proof?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Levi-Civita Tensor & Group Theory: Symmetry?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Group Theory, unitary representation and positive eigenvalues
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Injective endomorphism = Surjective endomorphism
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad Ray tracing, regarding Turner Whitted's original paper
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Algebra with Complex Numbers & Imaginary Unit
  • · Replies 44 ·
2
Replies
44
Views
7K
MHB Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Kernels and determinants of a matrix
  • · Replies 5 ·
Replies
5
Views
12K
Undergrad What is the minimum rank of a skew symmetric matrix?
  • · Replies 5 ·
Replies
5
Views
7K
Graduate Is Dimension 3 Enough to Prove Isomorphism Between Spaces?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Diagonalizable endomorphism has trivial null space
  • · Replies 6 ·
Replies
6
Views
2K
MHB Using matrix to complete the square
  • · Replies 4 ·
Replies
4
Views
3K
MHB Quasi-local commutative ring with maximal ideal M
  • · Replies 16 ·
Replies
16
Views
4K
Graduate F=ℝ: Normal matrix with real eigenvalues but not diagonalizable
  • · Replies 1 ·
Replies
1
Views
3K
MHB Maximal Ideals of K[X] in Commutative Algebra: A Helpful Guide
  • · Replies 8 ·
Replies
8
Views
6K
MHB Solve 3D Vector Equation: x-int=3, z-int=-1; (x,y,z)=(p1,p2,p3)+t(d1,d2,d3)
  • · Replies 5 ·
Replies
5
Views
3K
MHB Zero-Trace Symmetric Matrix is Orthogonally Similar to A Zero-Diagonal Matrix.
  • · Replies 5 ·
Replies
5
Views
5K
Graduate What is the New Definition of Conformal Transformations?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Number of jordan blocks in Jordan decomposition
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Basic Question: Order of permutations in Sn
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad How to visualise bilinear form and inner products?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Short Exact Sequences 0→A→B→C→0: Explained
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Cosets: difference between these two statements
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Do Orthogonal Subsets Spanning the Same Subspace Prove Equality?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate SVD Low-Rank Approximation Algorithm
  • · Replies 8 ·
Replies
8
Views
3K
MHB Prime Ideals in K[X] - Commutative Algebra Exercise 3.22 (ii)
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Projective Plane: Understanding "Set of Equivalence Classes" & Deleting Origin
  • · Replies 6 ·
Replies
6
Views
3K
MHB Proving End($K^2$)=K for A-Module $K^2$
  • · Replies 7 ·
Replies
7
Views
2K
Graduate How Can I Publish My Beal Conjecture Findings?
  • · Replies 1 ·
Replies
1
Views
3K
MHB Linear Dependency: Max Size of Subset of Vectors
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Is it possible to express all mathematics through atomic pieces of computation?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Compute Ideal Generated by Matrix 3x3
  • · Replies 5 ·
Replies
5
Views
2K
MHB Is \( A \) Isomorphic to \( \dfrac{R<X,Y>}{((X^2+1)X,(X^2+1)Y,YX)} \)?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Is this homomorphism, actually isomorphism of groups?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Algebra: Generating C as an R Algebra Subject to i^2=-1
  • · Replies 5 ·
Replies
5
Views
2K
MHB Why is Sharp's Lemma 1.10 crucial for understanding R-algebras?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Linear algebra, when does the implications hold?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Maximal Ideals K[X]: Solving Exercise 3.6 w/ R.Y. Sharpe
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Multiple Choise Questions in Calculus/Algebra/Electromagnetism
  • · Replies 2 ·
Replies
2
Views
2K
MHB Number of elements and subgroups
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Understanding Low Rank Approximation with SVD: A Comprehensive Guide
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Are Matrix Multiplication Rules the Same for Composing Linear Transformations?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Matrix transform- about origin, then angular rotation
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Are orthonormal eigenbases unique?
  • · Replies 5 ·
Replies
5
Views
3K
MHB What is the fastest method for computing determinants?
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Set of invertible matrices with real entries
  • · Replies 3 ·
Replies
3
Views
2K
MHB Prove These 3 Statements About A Matrix: Rank of Adjoint
  • · Replies 1 ·
Replies
1
Views
9K
Graduate Is $\mathcal{R}$ Lie Group Without 0?
  • · Replies 11 ·
Replies
11
Views
2K
MHB Is the Orthogonal Complement of an Invariant Subspace Itself Invariant?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Orthogonal Projections vs Non-orthogonal projections?
  • · Replies 1 ·
Replies
1
Views
3K
MHB Prove that every nonzero vector in V is a maximal vector for T.
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Product of two Minkowksi metrics
  • · Replies 1 ·
Replies
1
Views
1K
MHB Distance Between a Subspace and a Vector
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determinant of a unit columns matrix
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Call for help in finding approximate inverse matrix
  • · Replies 10 ·
Replies
10
Views
2K
MHB Distance from a vector to a subspace
  • · Replies 6 ·
Replies
6
Views
12K
High School Comparing Vectors: Orientation vs. Direction
  • · Replies 3 ·
Replies
3
Views
2K
MHB Elementary Algebraic Geometry - D&F Section 15.1 - Exercise 15
  • · Replies 9 ·
Replies
9
Views
2K
MHB What is the annihilator of a tensor in vector space V?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Jordan Normal Form of Unitary Transformation
  • · Replies 2 ·
Replies
2
Views
2K
MHB The Existence of Symmetric Matrices in Subspaces
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding Basis of the Quotient Space
  • · Replies 9 ·
Replies
9
Views
7K
MHB Semigroup Structure: Exploiting Non-Finitely Generated Monoids
  • · Replies 7 ·
Replies
7
Views
2K
MHB Solving Systems of Linear Equations with ljx.m
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is the Matrix R Necessarily Lower Triangular in Matrix Decomposition?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Sizes of kernels of homomorphisms
  • · Replies 1 ·
Replies
1
Views
1K
MHB Algebraic Geometry - D&F Section 15.1, Exercise 24
  • · Replies 1 ·
Replies
1
Views
2K
MHB Parametrization of a Reduced Matrix
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Open Conditions for Matrix Groups: Understanding the Role of det(A)≠0
  • · Replies 6 ·
Replies
6
Views
2K
MHB Partial Derivatives of Matrix/Vector Function: An Easier Way?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Abstract algebra: elements of fiber writable as
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Difference between line vector and free vector
  • · Replies 3 ·
Replies
3
Views
4K