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.
Possible Expressions for Matrix Rotation Reduction
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Proving Basic Exponent Properties for a Group
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Construct resultant for 3 polynomials
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What Is a Multilinear Function in Multilinear Algebra?
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MHB The Orthogonality of Vectors and Matrices
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Understanding Ladder Operators in SU(N) Quantum Mechanics
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MHB Find Parameter Producing Line l Through Points P and Q
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MHB Orthogonal Rotation: Get Info & Tips
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Eigen values and Eigenvectors for a special case of a symmetric matrix
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MHB Calculating Orthogonal Projection: Proving AD and Formula Progress | \pi\rangle
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Field extension that is not normal
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Commutator subgroup a subgroup of any Abelian quotient group?
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MHB Confirming Understanding of an Orthonormal System
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MHB Calculating Length and Angle of Vectors in an Orthogonal System
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MHB Linear Independence of Vectors: Why Determinant ≠ 0?
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Normalizers and normal subgroups.
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Is X^M-N the Minimal Polynomial of Irrational Root \sqrt[M]{N} in \mathbb{Q}[X]?
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MHB Solving a Matrice Equation: AX=B
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MHB How Do Basis and Vectors Work in Linear Algebra?
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MHB Proof of Gauss' Lemma - Issue re Proof
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MHB What Are the Rules for Determining the Determinant of a 4x4 Matrix?
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Find the symmetric matrix from eigen vectors
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Need help understanding Remez Algorithm and Chebyshev Polynomials
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What Are the Key Applications of Group Theory in Mathematics?
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Computing determinants: Allowed shortcuts?
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User-defined orthonormal basis
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What Does R^m -> R^n Mean in Notation?
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MHB Image, Range, and Matrix of a Linear Transformation
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MHB Why Are These Matrices Not Invertible?
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MHB How Do You Convert a Cartesian Equation to a Vector Equation in R3?
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MHB Conditions on Matrix Imply Conditions on Elements
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MHB MHBCalculate A^17: Powers of Matrices
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Orthogonal polynomials are perpendicular?
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Distinct zeros of irreducible polynomial
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Zero as an element of an eigenvector
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MHB Are GCDs Always Defined in Integral Domains?
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Maximizing quantity which is a product of matrices/vectors
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MHB Form of symmetric matrix of rank one
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Is the Dot Product Definition Valid Only for Orthogonal Coordinates?
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Transition Matrix and Ordered Bases
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MHB Can Subgroups Form a Group by Union Without Containing Each Other?
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MHB Polynomial Rings - Gauss's Lemma
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MHB This suggests that both H and K are normal subgroups of L. What am I missing?
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MHB Understanding Vector Mechanics with a Particle in 2D
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How do we prove the distributive property of multiplication?
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MHB Is the limit vector $x$ in the subspace $F$?
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Fair to say there are twice as many square matrices as rectangular?
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What exactly is a vector in and 5-D and more dimensions?
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Dimensions of Matrices Range (equalities).
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MHB Proving that a ring is non a PID
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A good linear algebra text book?
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MHB Help Proving Isomorphism of a group
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MHB Rings of Fractions and Fields of Fractions
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Solutions to cross product, a x u = b
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Orthogonality Problem (From Fourier Analysis Text)
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MHB Prove a ring: showing an element has an additive inverse
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MHB Proving statements regarding invertible matrices
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MHB What is the problem in this Proof
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Easy test if unitary group is cyclic
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What are the conjugacy classes of subgroups of Z X Z?
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MHB What are the ideals of the ring Z[x]/<2, x^3 + 1>?
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Where can I find helpful resources for abstract algebra?
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MHB Greatest common divisor of two polynomials
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MHB Polynomial Rings - Z[x]/(x^2) and Z[x^2 + 1>
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Why Are Symmetric & Non-Symmetric Matrices Not Unitarily Equivalent?
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Generalization of Chinese Remainder Theorem
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MHB Finite abelian group textbook help
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Do all complex functions have orthogonal real and imaginary parts?
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MHB Closure of a Subgroup of GL(2,C)
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Why is Linear Algebra easier to understand than Calculus?
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Eigenvalues of nonlinearly coupled equations
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Solving Eigenvalues: Complex Numbers Solutions
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Why this paradox in calculating eigen values for T*T ?
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Why Do Rank 1 Matrices Have Eigenvalues 0 and Trace?
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MHB What Does Reducing Z[x] Modulo the Prime Ideal (p) in Polynomial Rings Mean?
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Presentation of a group to generators in A(S)
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Solutions to Ax=b lie in row space?
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Hilbert Space Interpretation of Fourier Transform
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Is the Dual Space a Subset of V?
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Arctangent2 without square rooting?
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A three-gear alignment problem, simultaneous equations
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MHB Integral Domains and Principal Ideal Domains (PIDs)
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How do I show that the vectors of an invertible MX are indepedent?
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Determinant Function: Understanding Orientation
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Isomorphism between groups and their Lie Algebra
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Groups of order 12 whose 3-Sylow subgroups are not normal.
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How Does the Isomorphism Between Z_k and Aut(Z_n) Work?
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Elementary question about Dirac notation
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Any ideas for an explicit formula?
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Finding the least square solution with only positive coefficients
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Covariant and Contravariant Components of a Vector
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Can't understand this statement about factor rings
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MHB Integral closure in finite extension fields
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How Can You Represent Determinants Using Permutations?
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My Proof of Structure Theorem for Finite Abelian Groups
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MHB Proofs about invertible linear functions
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MHB Principal Ideals - Need for a ring with identity or a unity
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Proving Invertible Matrix Theorem: A^TDA=D
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MHB Principal ideal in a ring without identity
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MHB Is the Analysis of Principal Ideals Correct?
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