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.
Solving tri-linear interpolation parameters
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Does every element of order 2 in a finite group have a complement in the group?
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Why do we say morphisms preserve the structure/operations?
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Linear combination of two numbers
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How Can I Infer the Expression of A in a Non-Trivial Solution?
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Are there primitive roots in Z_32?
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MHB Isomorphism Between Vector Spaces: A Real Life Analogy
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Dropping a rule in vector spaces
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Intuition for Quotient Ring in Polynomials
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Dimension of the null space of A transpose
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Finding permutations of a stabilizer subgroup of An
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Number of positive divisiors with gcd condition
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A link for Linear Algebra Problem solvers REA
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Modular Arithmetic and Diophantine Equations
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Finding Roots of Bivariate Polynomial Surfaces: A Slice Technique Approach
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Can Two Intersecting Planes be Found from a Parametric Line Equation in ℝ^{3}?
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MHB Basis & Dimension of 2x2 Matrix Subspaces: W1 & W2
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Using Determinant Identities to solve
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Does n*a ALWAYS mean to a + a + + a (n times) where + is the group operation?
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A Distribution Analysis formula.
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Infinite dimensional vector spaces without basis?
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MHB Answer: Anti-Symmetric Matrix: Necessary 0's Diagonal?
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What is the meanning of this propisition ?
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Equivalence of the nullspace and eigenvectors corresponding to zero eigenvalue
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A possible more general form of Euler's identity
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From a vector space to the projective space
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What are some applications of prime numbers other than cryptography
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A Theorem on Squares and Congruences
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Conjecture: There exists no number k s.t. k^2+2 is a multiple of 7
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Invertiable for all values of theta
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Intersections of axes and affine space
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MHB X^(2^n) + x + 1 is reducible over Z2 for n>2
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Redundancy in definition of vector space?
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Eigenvectors with at least one positive component
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Solution x spanning columns of A
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Proof that exists prime btw n<p<n
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Is the Taylor Series Method Valid for Proving the Irrationality of ln(π)?
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Affine Varieties and the Vanishing Ideal
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What is the proof of this theorem in linear algebra ?
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Operations over infinite decimals numbers
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Can Spherical Symmetry Techniques Extend Plane Symmetries?
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What Real Life Examples Exist for an Inverse Linear Transform?
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Understanding Scalar Transformations in Matrix Dimensions
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Linear Independence: Is this true?
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Generalizing Linear Independence: Beyond R^n and into Matrix Spaces
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MHB How can rotation matrices be used to motivate students?
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What is the best way to think about an R-algebra?
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Proof of ∏(√n) Increment for Centered Polygonal Numbers w/ Prime Index
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Groups of prime order structurally distinct?
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How Can One Visualize a Group?
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Determinant of row interchange proof
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Ring Homomorphism: unit in R implies unit in R'
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Is There a Predictable Pattern in Prime Exponent Series Gaps?
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Question about generator of cyclic group
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Characteristic - must be on an integral domain? Books disagree?
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Quotient of the Mutlplicative Monoid of a Ring
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Can Subgroups Have a Volume in Linear Matrix Spaces?
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Unique set of vectors normal to a hyperplane
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Tridiagonal matrices multiplication
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Equivalent Matrices: Definition & A=B
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Why is it not possible for the columns of a matrix to span R^2 even if
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Matrices and linear transformations.
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What is the Parametric Description of Span{u,v,w}?
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MHB Prove that such a permutation exists.
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Equivalence Relations in A={a,b,c,d}: Proving the Bell Number Theorem
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Cube Roots of 1 in Polar Form: Stephen's Question
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Determining wheter point lie on line
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MHB What is the Maximum Norm Proof for Matrix A?
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How did the idea determinants come up?
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Regularity of P and Markov chains
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A question about linear transformations
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Matrix Problem: Solving for H(^T)*H with P and H matrices
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Is x1+x2=x3+x4 a linear equation?
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MHB Determinants and Rank: Solving for det(A) Given Rank(A)=4
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Can one determine the surf/circumf with a geometrical figure
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Residues and non residues of general quadratic congruences
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Interseccion of two planes in R3
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How to find a basis for the vector space of real numbers over the field Q?
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Linear Functions: Showing Properties for Multi-Vars
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Dot product between arrays: basis representation of an image
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Examine Structurally Distinct Abelian Groups with Primary Decomposition Thm
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Are Vectors Parallel If Dot Product Equals Product of Norms?
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What does this definition mean ?
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Monoid of specifications for a group
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Which subspaces retain nondegeneracy of a bilinear form?
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Consecutive integers such that the prime divisors of each is less or equal to 3
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Dot and Cross Product from Rotation Matrix
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Is there a Whole Number Multiple of Pi Closest to a Whole Number?
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Proving Existence of Basis in Vector Spaces
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Linear dependence and independence; linear combinations
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Why is b considered an element of R^m in the Ax=b theorem?
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Logarithm of 2x2 Matrix: A General Guide
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How Do You Find the Inner Product of Vectors in Polar Coordinates?
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How Do You Find the Equation of a Plane Given a Point and a Perpendicular Line?
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Matrix corresponding to linear transformation is invertible iff it is onto?
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Proving the Group Properties of M, the Set of Nth Roots of Unity
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MHB Finding the Inverse of Symmetric Matrices with Non-Real Coefficients
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Understanding Vector Spaces: Properties and Applications
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Is it possible to define a basis for the space of continuous functions?
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Transforming a matrix to orthogonal one
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