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.
Why use the notation (s, a, b, c) for quaternions instead of (s, v)?
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Understanding the method to solve the cubic equation
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A Large scale eigenvalue problem solver
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MHB Split Short Exact Sequences - Bland - Proposition 3.2.6
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MHB How Do We Find the Embeddings of $\mathbb{Q}(\sqrt{2})$ in $\mathbb{R}$?
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MHB Proving Intersection of Ideals in $K[x_1,x_2,...,x_n]$
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MHB Show Irreducibility of $K^n$ Algebraic Set $V$ iff $I(V)$ is a Prime Ideal
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Question about row space basis and Column space basis
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MHB Are the Fields $\mathbb{F}_{2^2}$ and $\mathbb{Z}_2(a)$ Equal?
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Isomorphism between Clifford algebras CL(4,2) and CL(2,4)
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MHB Categories - Bland Chapter 3 - Problem 2 - Problem Set 3.1
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Can a One-Sided Identity Element in Groups Lead to Two-Sided Identity?
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MHB Categories - Bland Chapter 3 - Problem 1 - Problem Set 3.1
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Division Algorithm for Polynomials in R[x] confusing me
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MHB Showcasing $V(I \cap J)=V(I) \cup V(J)$ in Polynomials
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Roots of unity, Roots of complex equations of the form z^n = 1
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Nonhomogeneous System: Similar Coefficients & Solutions?
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Confusion about position operator in QM
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MHB Solving Supply & Demand Equations - Get the Price You Need!
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Number of eigenvectors for Hermitian matrices
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Is the Matrix B Positive or Not?
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Do Matrix Inverses Commute When Flanking Another Matrix?
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Free Modules: Bland Corollary 2.2.4 - Issue on Finite Generation
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Doubt about rotation isometry on the complex plane
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MHB Problem with idempotent matrices
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MHB Commutative rings are IBN-rings - Bland Proposition 2.2.11
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MHB Help with Paul E. Bland's Division Rings and IBN-rings Prop 2.2.10 Proof
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MHB Free Modules With More Than One Basis - Bland - Example 5, page 56
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Lie Groups, Lie Algebra and Vectorfields
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MHB Free Modules w/Multiple Bases: 2nd Issue w/Example 5 (Paul E. Bland)
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MHB Understanding the Standard Free Right Module on a Set X?
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MHB Is $C[x,y,z]/<y-x^2,z-x^3>$ an Integral Domain?
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Solving Cyclic Group Questions: How Many Elements of Order What?
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Our Old Friend, the Twin Primes Conjecture
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MHB Endomorphism Rings - Bland Example 7 - page 10
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MHB Free Modules - Bland - Proposition 2.2.3
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Is every diagonalizable representation of a group reducible?
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Proof of the twin primes conjecture
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MHB Free Modules: Solving Issue of Finite Generation Corollary 2.2.4
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MHB Free Modules - Another issue regarding Bland Proposition 2.2.4
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Duality and Orthogonality: What's the Difference?
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Projection of a on b when a, b are complex
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Derivation of rotation isometry on the complex plane
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MHB Quadratic form, determine the surface
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MHB Free Modules - Another problem regarding Bland Proposition 2.2.3
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The adjoint representation of a semisimple Lie algebra is completely reducible
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MHB Exploring Algebraic Sets: Finding Irreducibility and Prime Ideals
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Some questions about group representations
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MHB Proving Maximal Ideal of $\mathbb{C}[X,Y]$
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MHB Simple Issue with Submodules - Northcott, Proposition 2, pages 7-8
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MHB Sum of an Indexed Family of Submodules - Northcott, pages 8-9
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Is the Direct Product of Two Finite Cyclic Groups Cyclic
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MHB Question on rank-nullity theorem
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Zero Dimensional Null Space (What's the meaning of this?)
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How do you take a tensor product?
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MHB How to solve the following matrix rotation
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Definition of determinant for 2x2 matrix
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MHB Finding the Rank and Basis for a matrix
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MHB SEO) Discovering Matrix 2: A 3x2 Matrix Calculation and Its Applications
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Difference between orthogonal transformation and linear transformation
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MHB Why is the characteristic different from 2?
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Possible Number of Vertices for Graphs with Three Edge Connections
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Dihedral Group D_4: Denotations & Correspondence
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Some help understanding vector space
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Need help with some linear algebra questions
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MHB Finding the Matrix Aij: Cubic Root of 2, -4 Power of j & Sqrt of 3)
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MHB Surjectivity of a Free Module Homomorphism implies injectivity
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Proof of Left Cosets Partition a Group
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Are the Only Ideals in M(2, R) Trivial?
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MHB External and Internal Direct Sums - Bland - Rings and Their Modules
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Proving vectors are in the column space
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How can Lambert's equation be used to solve for x?
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For G = <a: a^100 = e>, find the following
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Solving Computations w/ Cycles: Permutations, Inverses, Orders
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MHB Problem about a group with two inner direct product representations
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MHB Elements of the form a/b in an integral domain - simple question
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Proof of Trace Orthogonality Relation for Matrices $\Gamma^A$
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MHB Find basis and dimension of the intersection of S and T
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MHB Find the image of a two variable function
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MHB Is it true these are theorems in Linear Algebra?
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Algebra experiment using cellophane
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Linear Algebra Matrix Transformation to plane
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Row and Column equivalent matrices
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MHB Modules - Northott: Proposition 1
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MHB Show that it satisfies the equation
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MHB Show $\|.\|$ is an Norm: Prove Triangle Inequality
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Factor Groups: What am I thinking about wrongly here?
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Is Matrix Addition Commutative?
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Modulus & Division: Last Digit of Numbers Explained
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MHB Can every subring of an algebraic extension be a field?
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How do I make a change of basis with tensors in multilinear algebra?
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Iterations of functions of noncommutative variables
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MHB Dimension and Basis of a Relation in R5
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MHB Find the coordinates of the expression
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MHB Find coordinates of f′, f′′, f′′′ in the basis
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MHB Showing Linearity of $\varphi$ for $K(a)$
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MHB What Is the Splitting Field for \(x^{p^{80}}-1\) Over \(\mathbb{F}_p\)?
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MHB Field extensions and degree of odd prime numbers
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Why equating two planes does not provide solutions?
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Artin - domains don't seem to match
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