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.
MHB Find $\det(A+B)$ given $\det(A)=4$
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Discrete or continuous spectrum?
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Connection between topoi and schemes
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MHB Comaximal Ideals in a Principal Ideal Domain
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MHB Prime elements in integral domains
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Derive an expression to find how many times an eigen value is repeated
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Showing V is the direct sum of W1 and W2
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Group Axiom Ordering: Proving Associativity First
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MHB Gcd of polynomials is 1. There is an nxn matrix with determinant....
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Proof that Determinant is Multiplicative for Commutative Rings
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Why Can Every Element of SO⁺(1,3) Be Expressed as an Exponential?
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MHB Proof of Inner Product in E with Orthonormal Sequence (n=positive integer)
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MHB Is the Inner Product Space in C[0,2] Satisfied by the Integral Equality?
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Geometric insight about rotations needed
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Proving a Linear Transformation is Onto
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General Proof of Cross/Dot Product
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Finiding a representative of the 2nd conjugacy class in A_n
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Difficult Number Theory question
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Scalars and determining subspaces
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MHB Relation between Hermite and associated Laguerre
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Nth term of prime number sequence
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Nonlinear Operators on Finitely Generated Vector Spaces: Group Property Example
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MHB Is the Exponential of a Linear Operator Defined?
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Is Dirac Delta a Function or a Distribution?
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When do SO(2) actions on the circle in the plane determine a metric?
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Understanding Linear Perceptrons and their Decision Boundary in Neural Networks
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Possible Matrix with Equal Row and Column Sums?
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Global position and orientation of a point relative to another
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How to solve a problem involving modulus
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MHB Is the Product of Two Diagonalizable Matrices Always Diagonalizable?
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Sketch Conics: Motivating Students to Learn Cross Products
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MHB Sketch Conics: Motivating Students to Learn Cross Product Terms
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What is the significance of free products in group theory?
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MHB Use a subgroup lattice to compute a normalizer
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MHB Identify isomorphism type for each proper subgroup of (Z/32Z)*
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Factoring x^3+y^3+z^3: Conditions & Solutions
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Determinant of product of matrices
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MHB Vector Triple Product: Simplification Possible?
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MHB Does the permutation group S_8 contain elements of order 14?
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MHB Comparing Matrices: A-B>0 Positive Definite?
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Is There a Ring Homomorphism for All Unital Rings in Evaluation Homomorphism?
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MHB Schreier's Lemma Proof not clear.
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Can A>B Be Determined by A-B>0 for Matrices?
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Combine two pitch, yaw, roll rotations
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MHB Can Rank of A Determine Rank of A+A²+A³+A⁴?
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What Iterative Method is This?
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What does this answer mean? (continuous functions)
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One-to-one linear transformations
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Finding smallest solution to modular equations
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What Is an Integer Coefficient of Degree n in a Polynomial?
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MHB Understanding Dominant Matrices for Year 11 Students
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Are generators preserved under homomorphism?
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Quadratic Forms: Beyond Sketching Conics
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Are There Any Other Prime Solutions to the Equation x(x+1)+y(y+1)=z(z+1)?
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Largest Prime Number Found: 17,425,170 Digits Long
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Proving ABC^TA^-1 = CB: Step-by-Step Guide
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Solve SU(2) Parametrization Problem w/ Westra's PDF
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Factoring Method: Learn How to Use It
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MHB Solve Equation 5x - ||v|| v = ||w||(w-5x)
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MHB Best method for LU decomposition
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What Are the Strangest Vector Spaces You Can Imagine?
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Block matrix transformation of specific form
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Determine if vector b is a linear combination of vectors a1, a2, a3.
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How can I understand the equation for bicubic interpolation?
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What is a Convex Hull and How Does it Relate to Positive Definite Objects?
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Is A=5 and A=x Linear Operators?
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Orthonormal basis functions for L^2(R)
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MHB Quadratic Forms: Beyond Sketching Conics
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Can You Help Prove These Mathematical Identities?
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List the things f has to do to be a homomorphism
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Why are these functions commutatives?
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Not Satisfied with Linear Algebra Theorem
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Mapping an isomorphism b/w 2 grps
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Log expansion for infinite solenoid
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Why is a matrix singular if the determinant is zero?
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Finding which direct sum of cyclic groups Z*n is isomorphic to
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MHB Surjective and injective linear map
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MHB Which one of these two statements is wrong ?
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Efficient way to find which element of Z*n has largest order?
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What Are Graded Groups and How Do Generators and Degrees Function Within Them?
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MHB Linear Independence: Solving u,v,w Vector Questions
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Is every matrix diagonalizable if we allow complex entries?
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Challenging System of Equations (4 Variables)
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MHB Prime Ideals and Maximal Ideals
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MHB Proof about inner automorphism of a group
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Pisano Periods - Fibonacci Numbers mod p
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Can this number theory problem be solved purely algebraically?
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What is the definition of a 'true vector'?
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Convert Files: Change Formats Easily
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MHB Linear Map Problem: Proving Equivalence of a & b
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Explaining Missing Decimal Numbers 3, 6 & 9 in Calculations
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The rank of a block matrix as a function of the rank of its submatrice
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Is the Mean of a Sum of Randomly Chosen Numbers Always 1?
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Geometrical Interpretation of V in Span S
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Existence of a function for the n-th prime
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Does Z*(n) always have a generator?
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MHB The union of an ascending chain of subgroups is a subgroup
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Square root of a squared block matrix
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What kind of form is this general solution of a system?
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Solving for x in y = Tan(x): A Last Resort
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