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.
Undergrad When to use RREF in finding Eigenvectors
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Graduate If F is inner automorphism , what does this mean ?
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Graduate Are All Generating Sets in a Free Group Equally Cardinal?
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Undergrad 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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Graduate How do I use Chinese remainder theorem to solve for x mod 683 in Cryptography?
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Undergrad If A is singular; solution space of Ax=b
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Undergrad Dot product, is (a.b).(a.b)=(a.a).(b.b) ?
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Undergrad How do I calculate the new coordinates after rotating the coordinate axes?
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Graduate How Do We Define Stability in a Dynamically Growing System?
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Graduate Determinant of enlarged Correlation Matrix
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Graduate 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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Undergrad Linear Algebra (Symmetric Matrix)
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Undergrad What is a Quotient Group? A Simple Explanation
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Graduate How to solve for solutions to the diophantine 5b^2*c^2 = 4a^2(b^2+c^2)
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Undergrad Can anyone give a common-sense explanation of singular values?
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Graduate How do I solve a Jacobian problem involving a determinant?
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Graduate 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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Undergrad Basis/Unit vectors in other coordinate systems
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Undergrad Understanding L U Factorization to Solving Linear Systems
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Graduate Help me understand this proof of R^infinity's infinite-dimensionality
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Graduate The Cartan matrix in order to find the roots.
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Undergrad How Can Whole Numbers Be Defined Without Addition?
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MHB Possible title: Linear Optimization Problem: Finding Optimal Solutions
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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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Graduate What Is the Significance of 3.5036799918564934004113 in Mathematics?
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Graduate What Makes a Hermitian Matrix Positive Definite?
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Graduate Derivative of matrix square root
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MHB Proving Field Isomorphism: $\sigma (x) = x$ for $x \in K$
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Graduate 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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Graduate Irrational circles about the orgin
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Graduate 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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Undergrad Deriving the algebraic definition the dot product
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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 What is the definition of dividing vectors in R^2 using points P, Q, R, and S?
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MHB O(G)=56. Sylow 2 subgroup has all its elements of order 2.
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Undergrad Angle between vector and its transpose
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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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Undergrad Determinant is independent of row/column
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Undergrad Learning Eigenvectors & Linear Differential Equations in 24 Hours
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Undergrad A is not square but rank(A) = rank(A') ?
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Graduate 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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Undergrad The question is , if f(n)= 1+10+10^2 + + 10^n , where n is
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Graduate Inverse of a positive semi-definite matrix?
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MHB Linear Combinations and description geometrically
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Graduate Completing the basis of a matrix, Jordan form related
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Undergrad 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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Graduate Is a Zero Row Necessary in the Square Root of a Zero Matrix?
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Undergrad Non-square matrices and inverses
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Graduate Novel Multiplication and Division by odd squares
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MHB Matrix Multiplication: Is A Solution Possible?
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Undergrad Some questions about invertibility of matrix products
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Graduate Looking for a common solution of two systems
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Graduate Relationship between orbits and cosets
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Graduate Product and intersection of ideals of polynomial ring
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Graduate Large-scale eigen solver package for Fortran?
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Graduate Question on inner products between functions
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Graduate Can a Group Be the Union of Two Proper Subgroups?
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Graduate What is the meaning of A^(⊥) in a mathematical context?
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MHB LU Factorization: Introduction with Real Impact Example
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Graduate Coninvolution: A Powerful Property of Nonsingular Matrices
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Graduate 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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Undergrad LU Factorization: Motivating Explanation & Real World Impact
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Graduate Proving the dot product between these vectors is always the same value
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Graduate Question on isomorphism between addition and multiplication
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Undergrad Axis angle rotations and changing rotation values
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Graduate What is the dimension of eigenspaces in a function-based linear transformation?
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Undergrad Infinite and finite countable sets
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Graduate Algebra - Finding the Order of an Element from the Size if It's Conjugacy Class
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Graduate How the inner product changes under non-linear transformation
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Graduate Set of vectors with each subset forming a basis
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Graduate Number of lattice points between y=ax+b and y=x^2?
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Undergrad Linear programming: How to find extreme points and extreme directions?
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Undergrad Multiplying Complex Numbers: Understanding the Two Methods
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Graduate Isomorphism types of abelian groups
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Graduate Reference or explanation of zeta mellin transform in critical strip
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High School About the properties of infinity
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MHB Understanding the Relationship between Non-Members in Generated Subgroups
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Undergrad What is the length of the vector (1,i) and why can it still be normalized?
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Undergrad How Do You Correctly Multiply Complex Numbers to Verify Roots?
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Graduate Finding eigenvectors of a matrix that has 2 equal eigenvalues
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Undergrad If A is a tridiagonal Matrix , what does this mean ?
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Graduate Matrices satisfying certain relations
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Graduate Is the dimension of two vector spaces the same if they have equal cardinality?
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Undergrad Transpose a matrix whose elements are themselves matrices
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Undergrad It is defined that for any matrix A, [itex] A^{0} [/itex] is defined
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