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 Component is diagonal in the basis
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Graduate Does Preimage of Subgroup Under Homomorphism Form a Subgroup?
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Graduate Is it possible to solve for y using non-linear methods?
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MHB Proof of Exact Sequence Let $R$ & A Closed Set
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Graduate Embedding Group as a Normal Subgroup
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Undergrad Are the Right and Left Cosets Equal in a Group's Cayley Table?
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Undergrad How can I use linear programming to distribute S into two bins?
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Graduate Preliminary knowledge on tensor analysis
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MHB Can This System of Equations Be Solved for Variables x, y, z, and Any?
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Undergrad Non-Symmetric Matrix: Real Eigenvalues Examples
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Graduate Confusion about basis vectors and matrix tensor
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Graduate Equality involving matrix exponentials / Lie group representations
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Undergrad Matrix and transformation problem
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Undergrad What is the role of matrices in analyzing stresses and strains in materials?
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Graduate Is Tr(ABAB) Nonnegative for Symmetric Matrices A and B?
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Undergrad Does Universal Algebra Have Applications in Physics?
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Graduate Interesting Subspaces of ##L^p## Spaces
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Graduate Are fractional polynomials linearly independent?
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Graduate Matrix notation for Lorentz transformations
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Undergrad Perpendicular force from cross product
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MHB Glad I could help! Good luck with your studies.
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MHB Solving for D in a Confusing Matrix Equation | Invertible Matrices NxN
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Undergrad General expanded form of (x+y+z)^k
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Graduate Can Discriminants of Polynomial Equations Be Expressed Using Matrix Operations?
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Graduate Understanding Skew Symmetric Matrices for Physics - A Helpful Guide
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MHB Greatest common divisor of polynomials
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MHB Looking for an Example of an Amusing Theorem in Linear Algebra.
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Undergrad Inverse matrix notation question
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Graduate Position vector in curvilinear coordinates
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Undergrad What is the practical application of the trace of a square matrix?
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Graduate Lie-algebra representation powers - plethysms
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Graduate Compute the Quotient: [Z+Z]/[2Z+2Z]
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Undergrad Understanding Vector Transformations: Problem 1
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Undergrad Why does (a.b).c make no sense?
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MHB How can you simplify generated ideals in a commutative unital ring?
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MHB Counting Cosets: Clarifying Right & Left Cosets
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Graduate Proof of the Lindemann-Weierstrass Theorem
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MHB Integral Ring Theory: Proving Integral Extension Property for Quotient Rings
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High School Vectors - dot product and cross product?
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Graduate Rotation of Gridded Spherical Coordinates to the Same Grid
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Graduate Proof of the nontrivial expression
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Undergrad What are Eigenvectors and Eigenvalues in Relation to Matrices?
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Undergrad Can a dot product be negative in case of length?
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Graduate What are universal properties all about?
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MHB Are \( x-a \) and \( x-b \) Co-primes?
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Undergrad Where do the coefficients in this vector equation come from?
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Graduate Understanding the Relation Between Determinant and Trace in Physics Texts
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MHB Why do we conclude that p|exactly one of b0,c0?
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Undergrad Showing that V is a direct sum of two subspaces
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Undergrad Matrix multiplication - is this plausible?
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Undergrad Can any vector be in orthonormal basis?
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Undergrad How Does Cramer's Rule Relate to Geometry?
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Graduate How to prove if a recursive system is linear?
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MHB Are all subrings and units correctly identified in algebraic structures?
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Graduate Matrix Index Inversion: Clarification Needed
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Undergrad Identifying Largest Submatrices in a 0/1 Matrix?
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Graduate Generalised eigenspace contains the eigenspace?
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MHB Find the coefficient of x^{21} without calculating the product
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MHB Find all the zero divisors in a ring
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MHB Finding the Units of the Ring $R=\mathbb{Z}[w]$
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Undergrad Is it Necessary to Keep Zero Columns in an Augmented Matrix?
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MHB Do I Have to Show All Axioms to Prove a Set is a Ring?
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Graduate How to Efficiently Solve a Tridiagonal Matrix with Fringes?
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MHB Understanding the Linear Independence of Columns in a 3x5 Matrix
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MHB P divides all the coefficients of the terms with degree <8
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Graduate What is the General Expression for the Product of Two Matrix Exponentials?
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Undergrad Is "Multiplication Commutative in Rings?
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MHB Constructing a matrix version of the transformation algorithm?
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Undergrad Can anyone explain to me why eigenvector here is like this
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Graduate Solving Clifford Algebra Equation - Need Help!
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Undergrad Singular value decomposition and eigenvalue problem:
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Graduate Simple Proof for the existence of eigenvector
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Graduate What is a Collineation and How Does it Differ from an Affine Transformation?
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MHB Is $\Bbb Z_2 \times \Bbb Z_2$ a cyclic group?
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Undergrad Multiplication/division of matrices and vectors
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Undergrad Non-zero solution of a homogenous system
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Undergrad What is the geometric interpretation of the vector triple product?
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MHB Proving Even # of Transpositions for Identical Permutations
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MHB Partitions and equivalence relations
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MHB Some questions about the existence of the optimal approximation
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MHB What are Cyclic Subgroup Generators and How Do We Determine Them?
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Undergrad Questing about eigenvector order
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Graduate What is the Tensor Product and its Properties in Different States?
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MHB Linear Equations - Cost per Pound of Coffee Beans
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MHB Invertible matrices and encryption
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Undergrad Is the Cross Product Cancellative?
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MHB What Is the Annihilator of a Quotient Ring?
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Graduate Can Hexagonal Sampling Improve Efficiency of Kronecker Product Matrices?
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Undergrad How Do You Write the Trace of AB* as a Summation?
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Graduate Mathematics of circular shifts of rows and columns of a matrix
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MHB Finding Units in $\mathbb{Z}[i]$: Is There More Than $1, -1, i$, and $-i$?
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MHB Square Matrix Proof: Diagonal Entries & Properties
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MHB How Do We Prove That 'P' Doesn't Vary for Different Free Variables?
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MHB Finding smallest magnitude eigen value
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Graduate Are Hyperplanes Quotient Spaces?
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Graduate M-<M> for M operator: why not a mismatch?
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MHB Matrix multiplication simplified to Vector multiplication
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MHB Eigenvalues of Laplacian are non-negative
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MHB Ring Theory texts and "right notation" for maps/functions
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MHB Is There a Typo in the Refinement of Schanuel's Lemma in Passman's Book?
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