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.
Graduate Transforming a matrix to orthogonal one
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Graduate Identity in Subcategory C': Does it Coincide with Identity in Category C?
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Undergrad Kernel and Range: Understanding Linear Transformation in Algebra
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MHB Linear Algebra: Kernel & Range of Linear Transformation
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Undergrad Simple Proof for A-H Array Puzzle
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Undergrad Can you prove the formula for projection of a vector using dot products?
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Graduate Proving a relation between cross and dot products
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Graduate Consecutive integers divisible by a set of Primes
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Undergrad Why do we use double pipes to represent the norm of a vector?
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Graduate Mapping Conditions in Transformational Space
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Undergrad Proving that planes are parallel
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MHB If G is the union of 3 of its subgroups, show that they each have index 2
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Is Goldbach's Conjecture Finally Solved?
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Graduate Question on a proof by induction
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Graduate Can You Find the Unique Solution to These Simultaneous Equations?
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Undergrad Vector cross product with coefficients
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Graduate Matrices Formula for 10 by 10 Matrices
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Graduate Where do the vector space axioms come from?
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Undergrad What is the significance of the field Z₂ in mathematics?
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Undergrad Is there such a matrix operation
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Graduate Question on conjugate closure of subgroups
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High School Simple Proof That Division By Zero Is Impossible
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Undergrad Evaluate this algebraic expression f(a,b)
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Undergrad What Is the Solution Space for Ax=b in Linear Algebra?
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Undergrad What is the importance of linear transformations in linear algebra?
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Graduate Is this number countably or uncountably infinite as m approaches infinity?
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Undergrad Understanding basis and dimension
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Graduate Proving Integer Solutions for x^3 + y^3 = z^3
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Undergrad Quick check of 4 term polynomial factorised
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Undergrad Proving the Congruence of n^2 Mod 7: A Modular Problem in Number Theory
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Graduate Diagonolizing 5x5 Matrix by Hand
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Undergrad Scalar multiplication axiom, quick question
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MHB Using linear systems to solve problems (1)
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MHB Linear Transformation in Linear Algebra: Impact & Motivation
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Undergrad Does zero vector only exist in dim 0?
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Undergrad Finding if an integer is odd through Riemann or some function?
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Undergrad How Do You Solve This Linear System and Identify Free and Basic Variables?
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MHB Determining Basic and Free Variables in a Linear System
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Undergrad Diagonalizing a Matrix: Implications of Double Eigenvalues
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Undergrad Unsure Which Method To Solve Linear System Was Used
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Graduate Is it possible to linearize the non-linear equation in this linear programming?
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Undergrad Subspace vs Subset: Understanding the Relationship
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Graduate Solution of polynomial equations
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Graduate When Is L(S ∩ T) Not Equal to L(S) ∩ L(T)?
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Undergrad Linear systems: zero, one, infinite solutions
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Undergrad Badly Scaled Matrix? Explained with Examples
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Graduate Find point coordinate on 3D circle knowing three points
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MHB Using linear systems to solve problems (4)
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Graduate Homogeneous Eqn of Line given 2 homogeneous pointspoints
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MHB Using linear systems to solve problems (3)
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MHB Using linear systems to solve problems (5)
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Graduate Proving that the product of two full-rank matrices is full-rank
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High School A Question About Prime Numbers and Goldbach's Conjecture
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High School An odd coincidence or just nothing?
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Undergrad Proof- Vector fields form vector space
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Graduate Are There Only 3 Nontrivial Subgroups of Zp x Zp?
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Graduate How Do the Riemann Zeta and Dirichlet Eta Functions Interact?
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Graduate Proving the Existence of Direct Sums in Linear Algebra
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Graduate Rotation from axis to axis in 4 dimensions
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Undergrad Question about Applications 2 in Leon
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Undergrad QR Factorization: Uses & Benefits
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Graduate What is the Mathematical Definition of the Pauli Vector?
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MHB QR Factorization: Uses & Benefits
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MHB Maximal Ideal of Z[sqrt(-19)]: Showing Why (2, 1+sqrt(-19)) Works
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Graduate Decompose matrix into outer product of vectors
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Graduate Is 11 a Prime in the Non-UFD Ring Z[sqrt{-5}]?
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Undergrad Is it worse an over or an under determined system of linear equations?
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Undergrad Need help understanding Linear algebra proofs (and linear algebra in general)
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Graduate Showing that the normalized eigenvector for a distinct eigenvalue is unique
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Undergrad Understanding the Proof of Dot Products: A and B Vectors Explained
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Undergrad Why Does Solving Matrices Lead to Incorrect Variable Identification?
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MHB How Do You Calculate the Determinant of a Matrix in Linear Algebra?
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Graduate Is the ABC Conjecture Solved? New Proof Claims Deep Connection to Prime Numbers
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Undergrad Question regarding cross products and determinants
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Graduate Question about projection matrices
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Graduate Transforming between square matrices of different order
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Graduate What is the mysterious identity that holds for primes and certain composites?
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Graduate Is h(n) - f(n) in o(g(n)) Given f(n) in o(g(n)) and g(n) in O(H(n))?
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Undergrad Which Mathematicians Pioneered Prime Numbers for Cryptography?
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Graduate Determinant of Transpose Operator
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MHB Finding Angle & Distance Between Polynomials: Exploring Inner Product Spaces
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Graduate Is Pi divided by E rational, and what other irrational numbers exist?
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Graduate Inner product of polynomials
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MHB Can You Solve These Advanced Determinant Problems Involving Matrices?
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Undergrad Making Graphs with Loops & Knots: Explained
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Undergrad What model best fits this data and why?
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MHB Prove Unique Identity in Ring: Solution Explained
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Undergrad Proving Linear Manipulation to Reduce to GCD of Two Numbers
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Undergrad Discovering formula for a sequence with recurring digits
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Undergrad Infinite solutions to homogeneous system?
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Graduate Basis of a subspace and dimension question
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Graduate Infinitely Presented, Finitely Generated Group
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Graduate Wronskian and linear independence
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Graduate Complex Powers of an Elliptic Operator
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Undergrad Solving: Vector Subspaces Question in R3
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Graduate Why is the special orthogonal group considered the rotation group?
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Graduate Is There a Quadratic Equation for Polynomials in Z_n?
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Graduate What is a Quasi Upper Triangular Matrix?
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MHB Introducing Inner Product Spaces: Real-World Examples
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Graduate Introducing Inner Product Spaces: Real Impact Examples
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