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 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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High School Multiplying a vector with Square Matrix vs. its transpose
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Graduate Trying to find a simpler way to calculate this function
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Undergrad Matrix Alalysis, Matrix Algebra, Linear Algebra, what's the difference?
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