Linear and Abstract Algebra Forum

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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.
How to construct a vector perpendicular to a bunch of known vectors?
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Does multiplication by an invertible matrix preserve convexity?
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Bijective Homomorphisms and Isomorphisms
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MHB What Value of 'a' Yields One, None, or Infinite Solutions?
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Use Gaussian elimination with back substitution?
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MHB Vector Spaces: Explained (2x2 Matrices)
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MHB Splitting Fields - Beachy and Blair - Example 6.4.2
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Reconstruct A from its reduced eigenparis
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Why Does Complex Mapping T(z) = Az + B Fail Linearity?
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Direct Sum and Direct Product: Understanding the Differences in Vector Spaces
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MHB Proving r*r=q in S, a Ring with Identity
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MHB Field Theory _ Dummit and Foote - Example 4 - page 516 - Simple Computation
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MHB Field Theory _ Dummit and Foote - Theorem 3
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Isomorphic Groups: Proving Theorem True?
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MHB Algebraic Integers - Rotman - Proposition 2.70 - pages 118 - 119
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Example of Completely positive map from M_n to M_m
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Hermitian of product of two matrices
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Diagonalization of 8x8 matrix with Euler angles
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MHB Calculate 11c-5d: Solving Exercise
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MHB How Does Theorem 2.68 Explain Finitely Generated Groups in Algebra?
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MHB Rotman - Theorem 2.64 - Irreducibility
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Trying to avoid the quartic formula
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MHB Exercise 2.47 on Page 114: Showing a Polynomial Has Root in \mathbb{F}_4 - Peter
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Notation for the Dual of a Vector Space
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MHB Rotman - Theorem 2.60 - Unique Factorization
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Notation for the nabla operator arguments
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MHB Plane algebraic curves - basic definition of affine plane
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MHB Is my solution for this exercise correct?
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MHB Group of units - Rotman - page 36 - Proposition 1.52
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MHB Why does it imply that if f is onto there are a ≠ e_1 with f(a) ≠ e_2 ?
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MHB Any two fields with 4 elements are isomorphic
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MHB Solve Exercise with Modulo: Is this Correct?
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Inner Product of Complex Vectors?
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Counting the distinct values of a modular mapping
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MHB Is \( R[x,y] \) Isomorphic to \( R[y,x] \)?
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MHB The subgroup of S_4 <σ,τ> is the whole S_4
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MHB Norm of Integrals: Bounding the Matrix Product
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Is My Tri-Quadratic Curve Fit Equation Accurate Enough?
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MHB If R is a domain , then units in R[x] are non-zero constants
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MHB R commutative ring then R[x] is never a field
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Solution of system of non-linear equations
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MHB The Category Grp - Aluffi - Section 3.3 - basic question/clarification
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How Can You Create a Universal Reflection Vector from the Origin?
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MHB Groups as Groupoids with One Object
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What is the Study of N-Spherical Geometry in Four Dimensions?
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Why Is the Spectral Family Defined This Way in Functional Analysis?
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Notation used in matrix representation of linear transformation
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What is the relationship between two vectors in terms of rotation and scaling?
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Squared gradient vs gradient of an operator
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Intersection of an ideal with a subring (B)
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Intersection of ideals with subring
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MHB Understanding Disjoint Cycles: $k_1$ and $k_2$
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College Loan Repayment Optimization Pt.1
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MHB Universal Properties - Quotients - Aluffi, Chapter 1, Section 5.
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Proof question: the sum of the reciprocals of the primes diverges
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Intersection of maximal ideal with subring
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Linear Programming - satisfaction only at least one constraint
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(Non)Isomorphism of V with V** in Infinite-Dimension Case
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What does it mean to say that something "is a gauge theory"?
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MHB What is the name of this theorem in Abstract Algebra
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Why Are the Eigenvalues of This Matrix A and A + φ²B?
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Eigenvalues / Eigenvectors relationship to Matrix Entries Values
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Verifying that a matrix T represents a projection operation
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Expected Value Partial Trance Density Matrix
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Relation between unit tangent/normal vectors, curvature, and Lin. Alg.
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MHB Why aren't there coprime integers?
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Galois Theory, Differential Equations, and Lie Groups?
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MHB Functions that are injective but not surjective
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MHB Commutativity in the linear transformation space of a 2 dimensional Vector Space
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Ideal of an inversable triangular matrix
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Function of operators. Series, matrices.
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MHB Definition of epimorphism and equivalence to 'surjectivity'
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MHB Find Sample Solutions for Underdetermined Systems of Linear Equations
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Inverse of a special matrix of arbitrary size
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Why Does Adding Two Polynomials from a Set Not Always Result in a Vector Space?
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Wronskian vs. Determinant in Determining Linear Independence?
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MHB A theorem on Quadratic Forms in Reid's Book not at all clear.
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Condition for a number to be a Fibonacci one
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Is There a Formula for Unit Eigenvectors?
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MHB What are the functions of a graph in relation to arrow composition?
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MHB What Is the Universal Mapping Property in Free Monoids According to Awodey?
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Tensors of Free Groups and Abelian groups
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MHB Abstract Algebra Sylow Subgroup
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Is A^k a Projection Operator if k is Even/Odd?
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MHB Is a Latin Square always invertible?
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Commutator of a group is identity?
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How to Mathematically describe a plane?
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Diagonalizing a Matrix A: The Definition and Process Explained
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Defining Functions on Tensor Products
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Newton's identities and matrices
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Fourier Transform, Discrete Forier Transform image processing
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Is G/H Always an Abelian Group if H is Normal in G?
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MHB Category Theory - Definition of Hom(X,X) in Awodey
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What Kind of Tensor Product is v=S:∇I?
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MHB Quotient rings and homorphic images
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MHB D&F, Ch 10, Proposition 30 - Proof that (3) ===> (4)
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How write a matrix in terms of determinant and trace?
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MHB Simple question of interpretation - D&F Ch 10 - Proposition 30
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Simple question of interpretation - D&F Ch 10 - Proposition 30
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Why is Understanding Column Space and Null Space Important in Linear Algebra?
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