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 Why Is the Index Shifted in Laplacian Eigenvalues?
- member 428835
- · Replies 5 ·
Is My Matrix Solution Correct?
- pHlawless
- · Replies 4 ·
Graduate Adjoint of an adjoint of a linear map
- "Don't panic!"
- · Replies 16 ·
Graduate Can Vectors Span Just the Unit Sphere in Spherical Geometry?
- crownedbishop
- · Replies 4 ·
Graduate Rubik's cube group element with the smallest order
- Ahmed Abdullah
- · Replies 11 ·
How to Solve a System of Three Equations with Three Unknowns?
- mkelly18790
- · Replies 1 ·
Proving Subspace: Basic Proof for $V(A)$
- nacho-man
- · Replies 7 ·
Graduate Why is ##Aut(C_8)## not a cyclic group?
- jimmycricket
- · Replies 1 ·
Graduate Every field is an integral domain?
- PsychonautQQ
- · Replies 2 ·
Graduate Attempting to better understand the group isomorphism theorm
- PsychonautQQ
- · Replies 4 ·
Properties of permutation of a set
- Kiwi1
- · Replies 5 ·
Vector Space - Proving Associativity
- Dethrone
- · Replies 4 ·
Why does λI - A give wrong eigenvalues for one eigenvalue?
- Yankel
- · Replies 7 ·
Factoring x^4+4x^3-x^2-16x-12 by long division
- ai93
- · Replies 3 ·
Graduate Mismatched dimensions in a tensor product with CNOT
- nomadreid
- · Replies 1 ·
Undergrad Difference between Tensors and matrices
- Superposed_Cat
- · Replies 7 ·
What Value of a Makes Two Linear Equations Parallel?
- ThomsonKevin
- · Replies 3 ·
Graduate What is the solution to the 1=0 paradox involving self-adjoint operators?
- ShayanJ
- · Replies 6 ·
Undergrad How does facial detection with matrices work?
- Superposed_Cat
- · Replies 1 ·
Graduate Kernel vector of statics Jacobian
- aaddcc
- · Replies 1 ·
Graduate Groups of Order 16 with 4-Torsion, Up to Isomorphism
- WWGD
- · Replies 10 ·
Graduate Understanding Cardano's method of solving Cubic equation
- PcumP_Ravenclaw
- · Replies 3 ·
Graduate When is the Frobenius norm of a matrix equal to the 2-norm of a matrix?
- GridironCPJ
- · Replies 8 ·
Linear Dependence in \mathbb{R}^4?
- bwpbruce
- · Replies 7 ·
Possible Echelon Form of Matrix
- bwpbruce
- · Replies 10 ·
Graduate Is Wedge Product the Same as Cross Product?
- hideelo
- · Replies 6 ·
Graduate Deducing Basis of Set T from Coordinates in Matrix A with Respect to Basis S
- Kraz
- · Replies 13 ·
Graduate Are \bigoplus and \times interchangeable in direct sum and direct product?
- jimmycricket
- · Replies 6 ·
Definitions of Functions and Spaces
- imfromyemen
- · Replies 1 ·
Graduate Prime ideal in noetherian integral domain lemma
- A.Magnus
- · Replies 17 ·
Elements of $\mathbb{F}_{2^2}: What Are They?
- mathmari
- · Replies 1 ·
Graduate How to show u x v in R^n space is orthogonal to u and v?
- logan3
- · Replies 4 ·
Possible Echelon Form of a Matrix
- bwpbruce
- · Replies 1 ·
Does the Subring Generated by Two UFDs Always Result in a UFD?
- Petek
- · Replies 1 ·
Graduate Smallest order with exactly 3 nonisomorphic Abelian groups
- Greg Bernhardt
- · Replies 6 ·
Please Critique My Solution Involving Linear Independence, Linear Dependence and Span
- bwpbruce
- · Replies 3 ·
Undergrad Null matrix can be an idempotent matrix?
- gianeshwar
- · Replies 9 ·
Graduate Generalization of combinatorial generating functions?
- Stephen Tashi
- · Replies 4 ·
Undergrad Is the Transpose Conjugate of a Unitary Matrix Equal to the Identity Matrix?
- andphy
- · Replies 7 ·
Graduate Irreducible linear operator is cyclic
- david34
- · Replies 3 ·
Undergrad Meaning of linearly dependent equations
- 22990atinesh
- · Replies 5 ·
Undergrad Linear independancy and orthogonality of vectors
- larusi
- · Replies 9 ·
Vectors in $R^3$: Is $\begin{bmatrix}4\\3\\0\end{bmatrix}$ Valid?
- bwpbruce
- · Replies 1 ·
Undergrad Why does a dependent system of 3 equations have a unique solution?
- 22990atinesh
- · Replies 4 ·
Undergrad Linear Algebra -finding determinant of a matrix
- Unusualskill
- · Replies 4 ·
Graduate Eigenvalue distribution relation
- nikozm
- · Replies 1 ·
Inverse Eigenvalues: A Puzzling Question?
- mathmari
- · Replies 2 ·
High School Matrices Math: What is a Determinant?
- yuenkf
- · Replies 5 ·
Graduate How can the kernel of a ring morphism be a subring?
- PsychonautQQ
- · Replies 6 ·
Graduate Why right cosets like Ha are not subgroups
- PsychonautQQ
- · Replies 4 ·
Undergrad Can a matrix have both zero and non-zero eigenvalues?
- Kubilay Yazoglu
- · Replies 8 ·
Undergrad The geometric shape of parametric equations
- Kubilay Yazoglu
- · Replies 1 ·
Undergrad Significance of Jordan Canonical Form
- thelema418
- · Replies 6 ·
Is $ \mathbb{Z}_p $ an Integral Domain and Principal Ideal Domain?
- evinda
- · Replies 3 ·
Noetherian Modules - Bland Proposition 4.2.3
- Math Amateur
- · Replies 2 ·
Northcott - Sums and Products of Ideals
- Math Amateur
- · Replies 2 ·
Graduate What Does the Second Index in SO(n,p) Represent?
- Aziza
- · Replies 3 ·
Graduate Antisymmetrization of multi-index tensors
- hrmello
- · Replies 2 ·
Finite Group Inverses: Proving $N_{ABC}=N_{CBA}$
- Fallen Angel
- · Replies 1 ·
Graduate Unitary Operation On A Complex Matrix
- Bashyboy
- · Replies 2 ·
Graduate What is the variance of the product of a complex Gaussian matrix and vector?
- nikozm
- · Replies 1 ·
Graduate Variance of a vector product/sum combination
- nikozm
- · Replies 4 ·
Graduate Transitive subgroup of the symmetric group
- hedipaldi
- · Replies 1 ·
Spanning Spaces with Linear Combinations
- IrinaK.
- · Replies 3 ·
Graduate Why does counting cosets seem to give G times H elements?
- sdembi
- · Replies 4 ·
Normal subgroups (Sylow Theorem)
- mathgirl1
- · Replies 2 ·
Northcott - Proposition 3 - Non-empty Inductive System
- Math Amateur
- · Replies 5 ·
Northcott - Proposition 3 - Inductive Systems Maximal Elements are Prime Ideals
- Math Amateur
- · Replies 4 ·
Undergrad Difference between span and basis
- MarcL
- · Replies 6 ·
Graduate Quotient field of the integral closure of a ring
- coquelicot
- · Replies 3 ·
Graduate Irreducible representations of SL(2,C)?
- pellman
- · Replies 4 ·
Why Are Maximal Elements in Omega Prime Ideals?
- Math Amateur
- · Replies 4 ·
What Determines the Galois Group of a Polynomial's Splitting Field?
- mathmari
- · Replies 3 ·
Graduate English name for the canonical factorization theorem
- nuuskur
- · Replies 1 ·
Graduate Valuations and places - decomposition and inertia group
- coquelicot
- · Replies 3 ·
Number of Elements in Finite Fields?
- mathmari
- · Replies 8 ·
Undergrad Linear operator, linear functional difference?
- Goodver
- · Replies 8 ·
Undergrad Why isn't a set of 2 vectors in ℝ³ always linearly dependent?
- MarcL
- · Replies 10 ·
Noetherian Modules: ACC, Finite Ascending Chain Definition - Bland
- Math Amateur
- · Replies 2 ·
Bland - Proposition 4.1.1 - (4) => (1)
- Math Amateur
- · Replies 4 ·
Graduate Is it possible to determine a basis for non-subspace spaces?
- Kubilay Yazoglu
- · Replies 8 ·
Graduate The exclusion of empty substructures
- 1MileCrash
- · Replies 5 ·
Symmetric and anti-symmetric matrices
- Yankel
- · Replies 2 ·
For which values of k is A^3 invertible?
- Yankel
- · Replies 3 ·
Graduate Complex line equation with condition |a| = |b|
- PcumP_Ravenclaw
- · Replies 1 ·
Noetherian Modules - Bland - Proposition 4.2.3 - (3) => (1)
- Math Amateur
- · Replies 7 ·
Noetherian Modules - Bland - Proposition 4.2.3
- Math Amateur
- · Replies 1 ·
Graduate Example of a local field of positive characteristic?
- zarei175
- · Replies 1 ·
Graduate A vector whose components are vectors?
- BiGyElLoWhAt
- · Replies 13 ·
Graduate Can someone explain fractional calculus?
- jack476
- · Replies 4 ·
Undergrad LU solve for matrix with zeros on diagonal
- nawidgc
- · Replies 2 ·
Graduate General Process for finding elements of a group
- Traceless
- · Replies 6 ·
Graduate Dual vector spaces and linear maps
- "Don't panic!"
- · Replies 8 ·
Modules - Generating and Cogenerating Classes - Bland - Chapter 4, Section 4.1
- Math Amateur
- · Replies 4 ·
Sum of Submodules - infinite family case
- Math Amateur
- · Replies 2 ·
Direct sum of free abelian groups
- mathgirl1
- · Replies 1 ·
Graduate Similarity Transformation Doesn't seem to work
- I_am_learning
- · Replies 3 ·
Undergrad More than 3 eigenvectors perpendicluar
- ss k
- · Replies 5 ·
Graduate Extending a Set of 3 Orthogonal Vectors to a Basis in R^5
- MathewsMD
- · Replies 3 ·
Undergrad Why is AB an Orthogonal Projection Matrix?
- MathewsMD
- · Replies 3 ·