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.
Singular value decomposition and eigenvalue problem:
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Simple Proof for the existence of eigenvector
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MHB Is $\Bbb Z_2 \times \Bbb Z_2$ a cyclic group?
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Non-zero solution of a homogenous system
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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 What are Cyclic Subgroup Generators and How Do We Determine Them?
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Questing about eigenvector order
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What is the Tensor Product and its Properties in Different States?
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MHB Invertible matrices and encryption
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Is the Cross Product Cancellative?
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MHB What Is the Annihilator of a Quotient Ring?
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Can Hexagonal Sampling Improve Efficiency of Kronecker Product Matrices?
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How Do You Write the Trace of AB* as a Summation?
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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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Are Hyperplanes Quotient Spaces?
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M-<M> for M operator: why not a mismatch?
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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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MHB Finitely Generated Modules and Artinian Rings
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MHB Change-of-Basis Matrix: Converting from (4,7) to (2,1) and How to Use It
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MHB Is a Prime Artinian Ring Simple?
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MHB Ring Epimorphism and Nil Radical
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MHB What are some recommended texts for studying algebraic topology?
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MHB New to Linear Algebra - LU Decomposition
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MHB Exact Sequences - D&F Section 10.5, Proposition 27
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MHB Exterior powers of a vector space and its dual space
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Higher dimensional cross products
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Finding satisfying matrix for a particular condition
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MHB How Can Group Homomorphisms Prove Injectivity and Surjectivity?
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Fourier transform vs Inner product
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MHB How to Calculate the Area Between Two Vectors in R^n?
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MHB Invariant subspaces of representations
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LTI system and sinusoids/complex exponentials
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MHB Category Theory - Isomorphisms of Posets
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MHB Solving for X in Matrix Equation: C^TA-XB=B^{-1}-X
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MHB Category Theory - is it just "abstract nonsense"
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Product of the conjugates of a polynomial
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Free groups: why are they significant in group theory?
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What Are the Key Properties and Questions About Free Modules?
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MHB Exact Sequences - Split Sequences and Splitting Homomorphisms
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Is the Jacobian Equal to the Quotient of Scale Factors?
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Unit vector in cylindrical coordinates
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Modifying a transformation based on yaw-pitch-roll or phi-theta-psi
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Solving nonlinear equations for yaw/pitch/roll given rotor/quaternio
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Is 1D Space a Subspace of 2D Space in Physics?
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MHB Exact Sequences - Isomorphisms Resulting from Exact Sequences
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(empirical) relation between MSE and condition number
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MHB Each equivalence class is a power of [g]
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Shilov's Linear Algebra Subspace Question
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Exploring the Generalization of Mercer's Theorem to Square Integrable Functions
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MHB Tensor Products - Example 8 - Dummit and Foote - Section 10.4, page 370
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MHB Understanding D&F Example 2: R/I Bimodule on Page 366
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Ideal representation for vectors/covectors
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What are reliable references for the theorem on integral extensions?
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MHB Simple Problem - Establishing an Isomorphism
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Free columns-combinations of columns?
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MHB Tensor Products - D&F page 369 Example 2
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Why Does Matrix B & C Result in Matrix A?
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MHB Tensor Products - D&F page 369 Example 3 - The map phi
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Finding a Transformation Matrix for Matching Signs in a Matrix
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MHB Simple Problem concerning tensor products
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Differences between row and column vectors
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Finding Angle Between Two Vectors Using Inner Products
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Proving the Falsehood of the Homomorphism Property for Ω:Zp^n→Zp^n
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Struggling with Linear Algebra: Where to Find Help?
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How Did the Definition of a Field Evolve to Require Commutativity?
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MHB Some help on a matrix question please.
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What is the difference between unit vectors v and r?
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Why this property of the product of two matrices
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MHB Tensor Products - Dummit and Foote Section 10.4, Example 2, page 363
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MHB Tensor Products - Dummit and Foote Section 10.4 Corollary 9
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Can We Subtract Matrices with Different Dimensions?
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MHB How do you find frobenius canonical form of a matrix?
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Theory for find the eigenvules of a matrix
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MHB Two sets generate the same vector space
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If A, B Hermitian, then <v|AB|v>=<v|BA|v>*. Why?
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Guidance: Convex hull, null space and convex basis etc
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MHB Could someone recommend me pure math linear algebra book?
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Is every norm preserved under a unitary map?
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MHB How to Prove Certain Matrix Operations and Understand Their Properties?
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MHB Greatest common divisor of a and b
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MHB Is There Only One Possible Z-Linear Map from T to T'?
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Hilbert, Banach and Fourier theory
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MHB Show all invariant subspaces are of the form
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Centerless Groups: Examples & Constraints
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MHB Tensor Products - The free Z-module construction
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Does there exist a canonical projection from Z^p-1 to Z_p
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MHB Tensor Products - D&F - Extension of the scalars
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Why do we learn Dual Space so early?
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Calculating Solid Angle Between Three Vectors: A Scientific Guide
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MHB Tensor Products - Dummit and Foote - Section 10-4, Theorem 8, page 362
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Row selection of matrix and the condition number
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Lie theory - sum of nilpotent ideals is nilpotent?
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