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.
Graduate Inner Product on a Real Vector Space
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Graduate Quick question regarding isomorphic groups?
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MHB What is the proof for the residual sum of squares problem?
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MHB Inner product in n-dimensional vector space
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Graduate Square matrix to the power of a imaginary unit
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Graduate Is the geometric multiplicity of an eigenvalue a similar invariant?
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MHB Prove matrix has all real eigenvalues
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Undergrad Way to re-express this equation by writing x and y separate?
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Undergrad Linear Systems with pseudoinverse matrix using SVD
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Graduate Question regarding Kronecker Delta
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Undergrad Algebra: How does [-x^2 -4x+4-1] become [(x^2+4x-4)-1]
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MHB Complex Conjugates/Proof by Induction
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MHB Automorphisms of the splitting field of the m-th cyclotomic polynomial.
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MHB Finitely Generated k-algebra - Nature of the finite generation - basic question
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MHB Can k(x) be Generated with Only One Rational Fraction?
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Graduate Transpose of the product of matrices problem
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Graduate Understanding the Relationship: Log, Traces, and Diagonalized Matrices
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Graduate Different ways to define vector multiplication?
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Undergrad Are vectors assumed to be with respect to a standard basis?
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MHB Why Does Vector Norm Use "Double" Absolute Value?
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Graduate Filter Near-Zero Matrix Elements: Reasonable?
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Graduate Binomial formula for spherical tensors
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Graduate Is it possible to design this?
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Graduate Nearly Singular Matrix Inversion
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MHB IBV16 Find a vector equation for the line
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Undergrad Recognizing even or odd permutation easily?
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Graduate Any pointer for analyzing this matrix?
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MHB Noetherian Rings - Dummit and Foote - Chapter 15 - Exercise 2a
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Graduate Linear Map T: Proving Existence of KerT=U if dimU≥dimV-dimW
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MHB IBV8 line L passes through the origin and is parallel to the vector 2i + 3j
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MHB Rings of the form R[X] - Ring Adjunction
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MHB Applying the distributive law....
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Undergrad System of linear equation in term of column vector
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MHB Does Z[root(-3)] Qualify as a GCD Domain?
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Undergrad What Is the Name of u=(3, 3, 3) Vector?
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Undergrad Why vector form is convenient?
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MHB Commutative ring | Exam question
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MHB *IBV6 Find vector eq of line passing thru (–1, 4),(3, –1). in form r = p + td
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MHB *IBV5 The vectors u, v are given by u = 3i + 5j, v = i – 2j
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MHB Prove/Disprove: $I+J$ and $I\cap J$ are Ideals of $A$
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Graduate Question about diagonalizable matrices
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MHB Question involving annihilators and solution spaces
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MHB Interesting problem with ideals and function
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Graduate Least k Such that a^k=1 in Finite Ring R
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Graduate Correspondence Theorem in Group Theory
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MHB How to Prove Certain Properties of Homomorphisms and Ideals in Ring Theory?
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MHB Exact Sequences - Diagrams that 'commute' - Example
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Graduate Low-Dimensional Matrix Approximation
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MHB Generalised Quaternion Algebra over K - Dauns Section 1-5 no 19
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MHB Generalised Quaternion Algebra over K - Dauns Section 1-5 no 18
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Graduate Question about Hermitian matrices
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Graduate Does the characteristic polynomial encode the rank?
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High School Finding the Sample Mean of a Matrix
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MHB Does the Isomorphism Between Field Extensions Determine the Minimal Polynomial?
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High School Learning About Number Systems: 2 Basic Questions
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MHB Can Set Union Have an Additive Inverse Like Real Numbers?
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Graduate Error in proof for symmetry groups?
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MHB Generalised Quaternion Algebra over K - Dauns Section 1-5 no 17
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Undergrad Why Does My Matrix Vector Multiplication in FORTRAN Not Work as Expected?
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MHB Matrix rings acting on right R-modules
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MHB Matrix rings acting on right R-modules - Dauns - Exercises 1-5 no 2
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MHB Is RA the Smallest Submodule of M Containing A?
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MHB Linear System-Coset: Solve Exercise & Learn
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Graduate What Defines a Simple Magma in Mathematical Structures?
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Undergrad How do we represent multidimensional data vectors on a 2D plot.
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MHB Direct Products and Sums of Modules - Notation - 2nd Post
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MHB Direct Products and Sums of Modules - Notation
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MHB Eigenvalues of similar matrices
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MHB How is the IBV3 Vector Applied in a Circle?
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Graduate Challenge V: Sylvester-Gallai Theorem, solved by Mandelbroth
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MHB Graphically solving 2X2 linear system and finding the line through 2 points
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Graduate Null Space of a Matrix and Its Iterates
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MHB What is the angle between vector a and b if a=-4i-2j and b=i-7j?
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Graduate Direct sum of the eigenspaces equals V?
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Undergrad How many equations are needed to solve this system?
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Undergrad Understanding the Correct Representation of the Cross Product of Vectors
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MHB Find vector w in terms of i and j
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Could someone me to read the following line
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MHB Positive definite matrix problems
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Undergrad Matrix multiplication, specifically elimination matrices.
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Graduate Question about vector space intersection properties
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Undergrad Is it possible one dimensional plane?
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MHB Solving Linear Transformations in R2: Step by Step Guide
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Undergrad Linear Algebra: Understanding Matrix as a Linear Transformation
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Graduate How does the characteristic of a field affect symmetric bilinear forms?
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Undergrad Polar unit vectors form a basis?
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MHB Positive Definite Matrices and Their Properties
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MHB Find the position vector of P
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Graduate Proving When a Tensor is 0: M \cong M \otimes K
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Undergrad Trying to understand dot product of two DIFFERENT vectors
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MHB A linear equation in 3 variables
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Graduate Euclidian and Hyperbolic rotations
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MHB Infinitely many least-square solutions
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Graduate Can Language Homomorphisms Map Truth Across Different Symbolic Systems?
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Undergrad Motivation behind eigenvalue and eigenvector
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Graduate The vector space of matrices that commute with A
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Graduate Does every permutation of group generators imply an automorphism?
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Graduate Remove Known Solution from System of Polynomials?
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MHB How Do You Determine the Image and Kernel of a Linear Map from R^4 to R^2?
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Graduate Vector Components and Translation
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