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.
Undergrad Why Rank is the Trace of a Projection
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Graduate Vector Spaces of Infinite Dimension
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Graduate Is Every Matrix Similar to Its Transpose?
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Graduate Properties of Gl(n,R); R a ring/division ring
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Graduate Is the Leech Lattice a Lie Group?
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Graduate What determines the orientation of a vector space?
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Graduate How to prove 'infinite primes' kind of problem
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Undergrad All Square Numbers Follow a Recursive Series?
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Undergrad Is Multiplication Really Just Repeated Addition?
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Graduate Orthogonal Matricies and rotations.
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Undergrad Recurrence formula in Pell's equation
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Undergrad SVD vs Eigenvalue Decompositon (Diagonalizability)
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Graduate The mapping to alternating tensors
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Undergrad What are the applications of group theory?
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Undergrad What are some recommended books for learning linear algebra?
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Graduate Determining if Subset is a Subgroup by using Group Presentation
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Undergrad How to extend a set to form a basis?
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Graduate Would Number Theory Collapse if Riemann's Hypothesis is Proven True?
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Graduate Can orthonormal columns lead to orthonormal rows in a square matrix?
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Graduate Quantifiers - does this order matter?
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Graduate Unique volume element in a vector space
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Graduate What is the rotation group of a cube?
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Graduate Convex set : characteristic cone
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Undergrad Is √N Always Irrational for Non-Square Integers?
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Graduate Grad textbook on abstract algebra
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Graduate Irreducible Polynomials over Finite Fields
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Graduate Primes and arithmetic progressions.
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Graduate Which is the Correct Jordan Form?
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Graduate Alt Tensor: If Alt(\omega)=\omega, Is \omega Alternating?
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Graduate Matrix & Basis: Find D Matrix for V
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Graduate Proving Normality of a Quotient Group: A Shortcut Method
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Graduate Invariance of scalar products on Lie algebras
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Graduate How many ways to express a prime (= 1 mod 4) into sum of 2 squares ?
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Undergrad Does the set of solutions for Ax=b form a subspace?
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Undergrad Does infinite solutions imply the row vectors are linearly dependent?
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Graduate What Are the Divisibility Patterns of Repunit Numbers?
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Undergrad Expressing Matrix Product Ax as Linear Combination of Column Vectors in A
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Graduate Meaning of Eigenvectors in a Graph
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Graduate When p(A)=0 iff p(B)=0 for any polynomial,why same minimal polynomial?
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Undergrad Why is the minimum norm solution commonly used for underdetermined systems?
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Graduate Can Any Matrix Be Similar to Itself Without Being a Scalar Multiple?
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Graduate Is Q^{-1}AQ^{-1} Always Hermitian?
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Graduate Triangular Similar Matrix question
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Undergrad Prove the column space of AB is contained in the column space of matrix A
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Undergrad Proving Invertible Matrix A Creates New Basis from {X1,X2,X3..Xn}
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Undergrad Is There Always a Solution for b^x - b^y to be Divisible by a?
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Undergrad Approximating an area by rectangles
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Graduate Classes of polynomials whose roots form a cyclic group
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Undergrad Finding basis and dimension of W = {(a,b,c,0)} where abc are real numbers
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Graduate Is \mathcal S Equipped with a Convex Structure?
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Graduate How Can You Accurately Draw the Riemann Xi Function Curve?
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Graduate Reciprocal basis and orientation
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Undergrad Proving AB & BA Have Same Characteristic Polynomial - Simple Ways
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Graduate Product of two systems of linear differential equations
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Undergrad What is a Closed Linear Subspace?
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Undergrad Finding values of t for which the set is linearly independent
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Graduate Understanding the Geometric Interpretation of the Gram-Schmidt Process
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Graduate Any fast way to compute the fixed vector of a Markov chain transistion matrix?
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Undergrad Does this set of polynomials span P3?
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Graduate Ken Ono and Hausdorff dimensions
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Graduate Congruence: Solving Let p be a Prime Number
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Graduate Row reducing the matrix of a linear operator
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Graduate Differentiability of eigenvalues of a positive matrix
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Undergrad Finding eigenvectors of similar matrices
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Graduate Is a 2x2 Complex Matrix with N^2=0 Always Similar to a Specific Form?
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Graduate Can you prove this inequality involving factorials and powers?
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Undergrad Is this possible or am I dumb - Solving for u
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Undergrad Testing for linear combinations using matrices instead of vectors
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Graduate Question about Dirichlet's theorem on arithmetic progressions
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Undergrad Intuition behind rotation matrices?
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Graduate Does AA^\dagger=I Imply A^\dagger is the Generalized Inverse of A?
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High School Simple explanation of a vector space
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Undergrad Does there exists a matrix who's product is itself?
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Graduate Self Adjoint and Anti-Self Adjoint questoin
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Undergrad Sum of digits without regard to place value?
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Graduate Column space of positive semidefinite matrix
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Graduate Coefficient of a polynomial in K[x] where K is a field of characteristic p
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Undergrad Matrix notation for vector stacking
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Graduate Why an Invariant Subspace Has an Eigenvector
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Graduate Conserving contiguity with a transposed progression
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Undergrad Understanding the Well-Ordering Theorem: A Simplified Explanation
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Undergrad Is 59,649,589,127,497,217 a prime no.?
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Graduate Matrix Representation of a linear operator
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Graduate Understanding Group C*-Algebras: Intuitive Expl.
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Graduate Finding Fraction Field of Z[1/2]
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Graduate Symmetric bilinear forms on infinite dimensional spaces
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Graduate Adjoint versus classical adjoint/any relation?
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Graduate Algebraic and Transcendental irrational numbers
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Undergrad Can Base 10 Logs be Evaluated Without a Calculator?
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Graduate How to Find the Basis of a 23D Subspace Using Maple or Matlab?
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Undergrad Is the Similarity Matrix S of A always the Identity Matrix?
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Graduate Linear Functionals, Dual Spaces & Linear Transformations Between Them
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Undergrad Why Was the Determinant Defined?
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Graduate Requirements for a*b = 0 implying a = 0 or b = 0
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High School One line function to find n mod 4 (n % 4)
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Undergrad Is a Matrix with a Zero Column Invertible?
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Graduate On the ‘Sub-Additivity’ of Principal Eigenvectors
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Graduate Simultaneous diagonalization while having repeated eigenvalues
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Undergrad A Measure of How un-prime a Number is?
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Undergrad How to make a vector function from a f(x) function
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