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.
Understanding the Usefulness of Vector Projection
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Some ideas concerning the Goldbach conjecture
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Explicit solution. Properties of vector norms
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MHB Repeated eigenvalues of a symmetric matrix
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Equality of Operators A & B on Hilbert Space H
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About interesting convergence of Riemann Zeta Function
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Why do we need to convert to a diagonal matrix?
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How can we use the Singular Value Decomposition (SVD) for image compression?
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MHB Exploring the Importance and Applications of Singular Value Decomposition (SVD)
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NxN-complex matrix, identified 2Nx2N-real matrix, determinant
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Repeated eigenvalues of a symmetric matrix
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What do we mean by 'Equivalent Projective representation ?
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Every feild has a subset isomorphic to rational numbers?
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Puzzled about characteristic polynomial output from my calc
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Is This Quadratic Form Positive Definite or Indefinite?
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How does the change of basis theorem work in linear algebra?
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Intuitive explanation for the general determinant formula?
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Eigenvalues of a complex symmetric matrix
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Infinite ring with exactly two non trivial maximal ideals
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Orthogonal set - Geometric interpretation
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Can you explain me why this is also isomorphism?
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How can I write the determinant as traces in this paper on complex matrices?
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Group action and equivalence relation
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When to use RREF in finding Eigenvectors
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If F is inner automorphism , what does this mean ?
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Are All Generating Sets in a Free Group Equally Cardinal?
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Non-homogenous secx ODE's and Euler eq's
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MHB Why do we need to convert to a diagonal matrix?
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How do I use Chinese remainder theorem to solve for x mod 683 in Cryptography?
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If A is singular; solution space of Ax=b
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How do I calculate the new coordinates after rotating the coordinate axes?
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How Do We Define Stability in a Dynamically Growing System?
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Determinant of enlarged Correlation Matrix
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Why Are Homomorphisms of Infinite Cyclic Groups Well-Defined?
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MHB Investigating Inconsistencies in Strogatz's Nonlinear Dynamics Book
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Linear Algebra (Symmetric Matrix)
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What is a Quotient Group? A Simple Explanation
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How to solve for solutions to the diophantine 5b^2*c^2 = 4a^2(b^2+c^2)
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Can anyone give a common-sense explanation of singular values?
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Irreducibility of Polynomial part deux
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MHB Unique x for all g in G such that $x^m=g$?
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Understanding L U Factorization to Solving Linear Systems
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Help me understand this proof of R^infinity's infinite-dimensionality
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The Cartan matrix in order to find the roots.
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How Can Whole Numbers Be Defined Without Addition?
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MHB Does R/N Form a Ring with Unity if N is a Proper Ideal of R?
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MHB Are Normal Subgroups and p-Groups Key to Understanding Finite Groups?
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MHB Direct product of abelian groups. Isomorphism.
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What Is the Significance of 3.5036799918564934004113 in Mathematics?
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What Makes a Hermitian Matrix Positive Definite?
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Derivative of matrix square root
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MHB Proving Field Isomorphism: $\sigma (x) = x$ for $x \in K$
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Are There Finite Solutions to Generalized Bocard's Problem for Non-Square A?
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MHB Proving Symmetry of Matrix Multiplication with Transpose | Step-by-Step Guide
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MHB Find Point E in Harmonic Range with A, B, C using Cross Ratio -1
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Irrational circles about the orgin
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What is Kern and its relation to skew Hermitian matrices?
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MHB Quotient Ring of a Field: Is it Trivial or Isomorphic to the Field?
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MHB Conditions for integral domain to be a PID
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MHB Is Every Homomorphism of a Field to a Ring One-to-One or Null?
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MHB O(G)=56. Sylow 2 subgroup has all its elements of order 2.
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MHB Invertible Matrices: Why These Statements Are Not Correct
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MHB Property of Matrix Multiplication
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Determinant is independent of row/column
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A is not square but rank(A) = rank(A') ?
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Why Do Prime Numbers Play a Role in Proving the Irreducibility of Polynomials?
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MHB Finite group of order 4n+2 then elements of odd order form a subgroup.
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MHB What is the image of \(ax+by+c=0\) under \(f\)?
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The question is , if f(n)= 1+10+10^2 + + 10^n , where n is
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Inverse of a positive semi-definite matrix?
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MHB Linear Combinations and description geometrically
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Completing the basis of a matrix, Jordan form related
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Linear Equation Solutions: A Systematic Approach for n1xn2 and n1xm2 Matrices
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MHB Proof: G/H1 is Isomorphic to H2/K for G with Normal Subgroups H1 and H2
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MHB Finding Eigenvalues for Different r Values
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Is a Zero Row Necessary in the Square Root of a Zero Matrix?
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Non-square matrices and inverses
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Novel Multiplication and Division by odd squares
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MHB Matrix Multiplication: Is A Solution Possible?
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Some questions about invertibility of matrix products
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Looking for a common solution of two systems
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Relationship between orbits and cosets
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Question on inner products between functions
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Can a Group Be the Union of Two Proper Subgroups?
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MHB LU Factorization: Introduction with Real Impact Example
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Coninvolution: A Powerful Property of Nonsingular Matrices
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Series form of the Laplace transform
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MHB Is the Action of Conjugation by Sylow 2-Subgroups Onto?
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Question on isomorphism between addition and multiplication
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Axis angle rotations and changing rotation values
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What is the dimension of eigenspaces in a function-based linear transformation?
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Infinite and finite countable sets
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Algebra - Finding the Order of an Element from the Size if It's Conjugacy Class
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How the inner product changes under non-linear transformation
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Set of vectors with each subset forming a basis
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Number of lattice points between y=ax+b and y=x^2?
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Multiplying Complex Numbers: Understanding the Two Methods
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Isomorphism types of abelian groups
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Reference or explanation of zeta mellin transform in critical strip
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About the properties of infinity
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