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.
Relation between covariance and rank
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MHB What Makes Hilbert Space So Confusing?
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MHB Eigenvalues & Eigenvectors of $t: M_2 \implies M_2$ Matrix
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Showing any transposition and p-cycle generate S_p
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MHB Help to understand this eigenvector case
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MHB Did my book do this wrong? (Vector Cross Product)
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Can a Group of Order 20 with Elements of Order 4 Be Cyclic?
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MHB How Do I Navigate Change of Basis in Linear Transformations?
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MHB Proving $(G,*)$ is a Group: Hints and Tips for a Simple Group Theory Problem
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Examples of infinite nonabelian groups not GL_n(G)?
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Finding pairs of operator-related vectors
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What is this Matrix question asking me to do?
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Degree of liberty of a matrix 2x2
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MHB Solving a system of linear equations with one unknown value
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MHB Why is the eigenvector of a row reduced matrix not always the zero vector?
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What Changes in the Third Pivot When a3,3 Shifts from 7 to 11 in Linear Algebra?
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MHB Find the error in the following argument
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MHB Algebras - k-algebra and R-algebra - reconciling two definitions ....
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Modern Algebra: Stabilizers and Conjugacy Classes of Dodec
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How to find generators of symmetric groups
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MHB Is There an Iff Relation for Polynomial Divisibility in the Ring F[t, t^-1]?
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MHB Is that correct so far ... ?Yes, that is correct. Good job!
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MHB When Does Such a Short Exact Sequence Exist?
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MHB Elementary Algebraic Geometry: Exercise 23, Sect 15.1 Dummit & Foote
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Planar angle between two vectors
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MHB Solve System of n Equations: Can You Help?
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MHB Elementary Algebraic Geometry: Dummit & Foote Ch.15, Ex.24 Coordinate Ring
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MHB Coordinate ring of an affine algebraic set - k[A^n]/I(V)
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MHB Arbitrary Subset of A^n - Is it necessarily an affine algebraic set?
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MHB Subsets in the Affine Plane and ideals of K[A^n]
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MHB Ideal of functions disappearing at (a_1, a_2, .... .... , a_n)
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Can the entries of a Matrix be elements of an unordered set?
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Finite field with hard discrete log for both groups
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Is this in general true (about projection matrices)?
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Linear Dependence/Independence and Wronskian
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Undergrad Could there be only one lower and one upper triangle?
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Software for drawing group lattice diagrams?
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Main Idea Behind Determinant & Its Purpose
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MHB Is the Lemma True for All Fields?
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MHB All basis' go to standard basis?
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Finite Field Structure: Prime Order Cyclic Group
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MHB Prime Ideal in a Commutative Ring - Rotman Proposition 7.5
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MHB Correspondence Theorem for Groups - Rotman, Proposition
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MHB Correspondence Theorem for Groups - Yet Another Question
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Is R^n Euclidean Space a vector space too?
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MHB Arithmetic for Quotient Groups - How exaclty does it work
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Question about Cyclical Matrices and Coplanarity of Vectors
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MHB Prove Nonzero Integer Lemma in $F[t, t^{-1}]$
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Determinant of 3x3 matrix equal to scalar triple product?
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Proving dependent columns when the rows are dependent
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How are the x1 and x4 values determined in the solution to the matrix equation?
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High School Vector Space Prob: Show Linear Dependence
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Beginner: understanding an answer
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Does Dirac notation apply to tensor product in tensor analysis?
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MHB Irreducible Polynomials and Quotient Rings - Rotman Proposition 3.116
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Mohr's circle and formula for eigenvectors
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Can quaternion group be represented by 3x3 matricies?
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Solve System of 5 Equations with Jordan's Matrix Properties
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MHB Function Field over k --> k(x) - Rotman Definition and Proposition 3.29
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MHB What is the Rank of the Direct Sum of Torsion-free Groups?
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MHB Looking for a new Lie Algebra text
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Can You Help With Finite Element Analysis in Cylindrical Coordinates?
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Finding elements in GL_2(R) with specific orders
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MHB Prime Field of a Field k - Rotman Theorem 3.110
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MHB Solving Linear Equations: 2 Planes from LAX - Cbarker1
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MHB Polynomial Rings _ Bland - Theorem 6.3.17
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MHB Polynomial Rings - Irreducibility
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Method to solve a coupled system of matrix equation
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Is it possible to find this number without brute force?
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MHB Why Do Functions \(X + UY\) and \(X - UY\) Have Zeroes Only at \(t = \pm 1\)?
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Linear algebra and choosing training vector
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MHB Why does $Y_n$ have that specific form?
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Why is the set of cosines and sines a vector space?
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MHB Understanding the Equivalence in Diophantine Relations
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Independent elements of matrices?
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MHB Rational Functions - Polynomials Over a Field - Rotman Proposition 3.70
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MHB UFDs .... Counterexample - I_8 = Z/8Z
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MHB Polynomials Over a Field - Rotman, Lemma 3.87
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Proof that all information can be coded in binary?
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Not (null T) is a subspace of V?
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MHB Euclidean Rings - Rotman Example 3.76
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MHB Properties of gcd's and relatively prime integers
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MHB Polynomials Over a Field - Rotman, Lemma 3.67
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MHB Why Is \(a\) a Unit in \(F[x]\) in Lemma 2 of Nicholson's Book?
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Change of Basis, Covariant Vectors, and Contravariant Vector
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MHB Factor Rings of Polynomials Over a Field - Nicholson, Lemma 1, Page 224
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MHB Finding unknown coefficients to give a unique solution in a linear system
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System of Linear Equations to Reduced Echelon Form
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Are there other symmetries on the plane besides the wallpaper and point groups?
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Equality of two elements of a hilbert space defined?
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MHB How Does Nicholson Apply Induction in Theorem 12 Proof?
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MHB Is {0} Considered the Smallest Integral Domain?
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MHB Bilinear transformation not working
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Eigenvalues/eigenvectors using householder and QR
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MHB Why Does \( p \) Divide \( f \) in Nicholson's Theorem 11?
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Representation of Lorentz algebra
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MHB Interpreting U={A|A^2=A, A is in M22}: Not a Subspace of M22
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MHB Factorization of Polynomials Over a Field - Nicholson Example 10, Page 215
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MHB Proving Vector Subspace $U \notin R^3$
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Asymmetry in MDS: Question on Unilateral Love & Hate
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