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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Infinite Direct Sums and Indexed Sets
- Math Amateur
- · Replies 9 ·
Graduate Inhomogeneous Linear System Solutions
- GregJ
- · Replies 1 ·
Graduate Unique solution to an arbitrary monotonic non-linear system
- dmytro
- · Replies 3 ·
Can Complex Numbers Solve This Linear System?
- toni07
- · Replies 9 ·
Undergrad Understanding Eigenspaces: Solving Exam Questions
- klingenberg
- · Replies 4 ·
Undergrad How can linear equations be solved using matrices?
- HMPARTICLE
- · Replies 6 ·
Universal Mapping Property of a Direct Sum - Knapp Pages 60-61
- Math Amateur
- · Replies 5 ·
Isomorphism Between External and Internal Direct Sums - Knapp Proposition 2.30
- Math Amateur
- · Replies 4 ·
Direct Sum of n Vector Spaces Over F - Knapp Proposition 2.31 - Pages 61-62
- Math Amateur
- · Replies 2 ·
First Isomorphism Theorem for Vector Spaces - Knapp, Theorem 2.27
- Math Amateur
- · Replies 10 ·
Graduate Is the Operation Linear and Bijective?
- schw
- · Replies 2 ·
Graduate Euclidean Algorithm Gaussian Integers
- dan280291
- · Replies 6 ·
Undergrad Best learning material for intro to Linear Algebra?
- WK95
- · Replies 9 ·
Why doesn't v + w belong to v + W in Schaum's coset example?
- Math Amateur
- · Replies 5 ·
Graduate Why parameterized solutions don't satisfy the original system Ax=b
- skujesco2014
- · Replies 2 ·
Graduate Vectors - are the definitions truly equivalent?
- 1MileCrash
- · Replies 17 ·
Graduate Positive definite inner product on Lie algebra.
- center o bass
- · Replies 3 ·
Graduate Any biinvariant metric proportional to Killing metric
- center o bass
- · Replies 7 ·
Ideals in Polynomial rings - Knapp - page 146
- Math Amateur
- · Replies 3 ·
Graduate Multidimensional fitting of two sets of data
- datameng
- · Replies 2 ·
Undergrad Understanding Vectors: Unit Vectors vs Kinematic Equations
- Mr Davis 97
- · Replies 1 ·
Graduate How does SVD filter important data from unimportant data?
- member 428835
- · Replies 10 ·
Undergrad Describing vectors in a different coordinate system
- Mr Davis 97
- · Replies 2 ·
Existence of Finite Fields with p^n Elements
- Math Amateur
- · Replies 18 ·
Graduate Adjoint representation vs the adjoint of a matrix
- center o bass
- · Replies 1 ·
Graduate How Do You Set Up Matrices for Cubic Spline Interpolation?
- gfd43tg
- · Replies 13 ·
Finite Fields - F_4 - Galois Field of Order 2^2
- Math Amateur
- · Replies 1 ·
Why Are the Roots of xf(x) and xg(x) Distinct in Finite Fields?
- Math Amateur
- · Replies 4 ·
Finite Fields and Splitting Fields
- Math Amateur
- · Replies 4 ·
Undergrad Why doesn't the parameterized solution satisfy the original Ax=b system?
- skujesco2014
- · Replies 1 ·
Graduate Meaning of ##\ominus## in Hilbert Spaces
- thegreenlaser
- · Replies 2 ·
Integral Domains and Characteristics - Char(D)
- Math Amateur
- · Replies 10 ·
Graduate Positive, negative, complex determinants
- divB
- · Replies 5 ·
Sum Binomials: Proving Numerical Test Result
- Bibubo
- · Replies 5 ·
High School Graphs for linear equations/inequalities
- kay
- · Replies 2 ·
Nature and character of Finite Fields of small order
- Math Amateur
- · Replies 16 ·
Undergrad Why does Calc&Graph show sin(π) as 1.22e-16 instead of zero?
- Adit
- · Replies 3 ·
Graduate Minimizing with constraints and linear function
- gfd43tg
- · Replies 6 ·
Graduate Are Faithful Representations the Most Interesting Group Representations?
- BruceW
- · Replies 3 ·
Graduate Short Exact Sequences and at Tensor Product
- WWGD
- · Replies 4 ·
Undergrad What's the difference between these 2 problems?
- Math10
- · Replies 6 ·
Undergrad How to construct a vector perpendicular to a bunch of known vectors?
- jollage
- · Replies 4 ·
Graduate Does multiplication by an invertible matrix preserve convexity?
- sloppyintuit
- · Replies 2 ·
Graduate Bijective Homomorphisms and Isomorphisms
- WWGD
- · Replies 2 ·
What Value of 'a' Yields One, None, or Infinite Solutions?
- TTaJTa4
- · Replies 3 ·
Undergrad Use Gaussian elimination with back substitution?
- Math10
- · Replies 3 ·
What set S makes 2×2 matrices equivalent to R^S?
- das1
- · Replies 1 ·
Splitting Fields - Beachy and Blair - Example 6.4.2
- Math Amateur
- · Replies 5 ·
Graduate Reconstruct A from its reduced eigenparis
- jollage
- · Replies 1 ·
Graduate Why Does Complex Mapping T(z) = Az + B Fail Linearity?
- seminum
- · Replies 3 ·
Graduate Why does V₁⊗V₂ seem lower-dimensional than V₁⊕V₂ in a simple example?
- Travis091
- · Replies 6 ·
Solve the system p1+4p2+8p3=26, 5p1+7p2=38, 8p1+12p2+2p3=66
- maarrcc1994
- · Replies 6 ·
Proving r*r=q in S, a Ring with Identity
- Achieve
- · Replies 4 ·
Field Theory _ Dummit and Foote - Example 4 - page 516 - Simple Computation
- Math Amateur
- · Replies 4 ·
Field Theory _ Dummit and Foote - Theorem 3
- Math Amateur
- · Replies 3 ·
Undergrad Do isomorphic groups have the same element orders?
- LagrangeEuler
- · Replies 12 ·
Graduate Intuitive understanding of quaternions
- Nathew
- · Replies 8 ·
Algebraic Integers - Rotman - Proposition 2.70 - pages 118 - 119
- Math Amateur
- · Replies 5 ·
Graduate Example of Completely positive map from M_n to M_m
- Genericcoder
- · Replies 2 ·
Undergrad Cross and dot product of two vectors in non-orthogonal coordinate
- anurag
- · Replies 3 ·
Graduate Hermitian of product of two matrices
- nikozm
- · Replies 2 ·
Graduate Diagonalization of 8x8 matrix with Euler angles
- Trifis
- · Replies 2 ·
Finding a generator of Z*_10 × Z*_22 and computing 11c-5d
- evinda
- · Replies 4 ·
How Does Theorem 2.68 Explain Finitely Generated Groups in Algebra?
- Math Amateur
- · Replies 1 ·
Rotman - Theorem 2.64 - Irreducibility
- Math Amateur
- · Replies 4 ·
Graduate Trying to avoid the quartic formula
- CRYS1SX18
- · Replies 3 ·
Why does x² + x + 1 have no root in ℤ₄?
- Math Amateur
- · Replies 4 ·
Graduate Notation for the Dual of a Vector Space
- Mandelbroth
- · Replies 2 ·
Rotman - Theorem 2.60 - Unique Factorization
- Math Amateur
- · Replies 5 ·
Graduate Notation for the nabla operator arguments
- carllacan
- · Replies 9 ·
Plane algebraic curves - basic definition of affine plane
- Math Amateur
- · Replies 2 ·
Verify solution for weighted sum of group theory properties
- evinda
- · Replies 8 ·
Group of units - Rotman - page 36 - Proposition 1.52
- Math Amateur
- · Replies 2 ·
Why does it imply that if f is onto there are a ≠ e_1 with f(a) ≠ e_2 ?
- mathmari
- · Replies 14 ·
Any two fields with 4 elements are isomorphic
- Math Amateur
- · Replies 5 ·
Proving a^p ≡ b^p (mod p²) from a^p ≡ b^p (mod p)
- mathmari
- · Replies 5 ·
Graduate Inner Product of Complex Vectors?
- kq6up
- · Replies 4 ·
Graduate Counting the distinct values of a modular mapping
- ing
- · Replies 1 ·
Is \( R[x,y] \) Isomorphic to \( R[y,x] \)?
- Math Amateur
- · Replies 7 ·
The subgroup of S_4 <σ,τ> is the whole S_4
- mathmari
- · Replies 8 ·
Undergrad Understanding 3D Rotation Transformations
- student6587
- · Replies 1 ·
Graduate The inverse of a banded matrix
- EngWiPy
- · Replies 2 ·
Norm of Integrals: Bounding the Matrix Product
- sarrah1
- · Replies 1 ·
Undergrad Is My Tri-Quadratic Curve Fit Equation Accurate Enough?
- mattskie
- · Replies 2 ·
If R is a domain , then units in R[x] are non-zero constants
- Math Amateur
- · Replies 1 ·
R commutative ring then R[x] is never a field
- Math Amateur
- · Replies 3 ·
Graduate Solution of system of non-linear equations
- JulieK
- · Replies 7 ·
Notation for inversion map in category Grp
- Math Amateur
- · Replies 1 ·
Graduate Constructing a reflection vector from the origin in linear algebra
- tanus5
- · Replies 14 ·
Groups as Groupoids with One Object
- Math Amateur
- · Replies 2 ·
Graduate What is the Study of N-Spherical Geometry in Four Dimensions?
- Hornbein
- · Replies 1 ·
Graduate Why Is the Spectral Family Defined This Way in Functional Analysis?
- thegreenlaser
- · Replies 1 ·
Graduate Notation used in matrix representation of linear transformation
- Seydlitz
- · Replies 4 ·
Undergrad What is the relationship between two vectors in terms of rotation and scaling?
- Jhenrique
- · Replies 11 ·
Graduate Squared gradient vs gradient of an operator
- carllacan
- · Replies 4 ·
Graduate Intersection of an ideal with a subring (B)
- coquelicot
- · Replies 4 ·
Graduate Intersection of ideals with subring
- coquelicot
- · Replies 5 ·
Understanding Disjoint Cycles: $k_1$ and $k_2$
- mathmari
- · Replies 4 ·
Graduate Finding payoff time from Laplace transform of loan equation
- avion105
- · Replies 4 ·
Universal Properties - Quotients - Aluffi, Chapter 1, Section 5.
- Math Amateur
- · Replies 13 ·