Linear and Abstract Algebra Forum

Post thread
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 What exactly is a position vector?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Resummation of the Harmonic series
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Calculating the Product of a Series
  • · Replies 14 ·
Replies
14
Views
4K
Graduate What is the true nature of linearity?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Homomorphism between commutative rings
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Question about centralizer and normalizer
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How to Perform a Cross Product on Polar Coordinates?
  • · Replies 7 ·
Replies
7
Views
10K
Graduate Can I Modify Order to Get X=I Matrix?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why is Linear Algebra Important and How is it Applied?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What Are Examples of Non-Abelian p-Groups?
  • · Replies 2 ·
Replies
2
Views
7K
Graduate What is the connection between L and gcd(k,n) in cyclic subgroups?
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Projection matrix onto a subspace
  • · Replies 1 ·
Replies
1
Views
7K
Graduate Is the Interval [a,b] Sequentially Compact?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Equivalence relation in complementary subspace
  • · Replies 8 ·
Replies
8
Views
4K
High School Is There a Simpler Method to Solve Similar Linear and Quadratic Systems?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Representing a dot product with Sums.
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Representing Square Matrices with Constant and Identity Matrix - A Guide
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad How to Find \vec{b} in a Cross Product Problem?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Cauchy-Bunyakovsky-Schwarz inequality
  • · Replies 5 ·
Replies
5
Views
9K
Graduate What Is the Size of GL_n(Z2)?
  • · Replies 9 ·
Replies
9
Views
7K
Graduate What do you call this homomorphism?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Question regarding sylow subgroups
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Questions about matrices and vectors:Why does the dot product of
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Finding the Smallest Subgroup of A_4 Containing Two Given Even Permutations
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad Proof of Equilibrium Solution for Algebraic Equation
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Proof Vector Spaces: Unique Vector Satisfying "u + 0 = u
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Solving Polynimals in the ring mod p^r
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Put an augmented matrix into RREF format
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Are a and b in G if ab is in G?
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Does the Exponential k Term Complicate Proving the Riemann Hypothesis?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Solving Congruences and the Relationship between (p^{l-1}) and (p^{l})
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Can a Non-Self-Adjoint Element Have a Real Spectrum?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Making a collection of sets as a group
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Linear Transformations: Find Eigenvalues & Eigenvectors
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Suppose T is a linear map and dim(Im(T))=k
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Can the 'Determinant' be Reversed for 2-by-2 Matrices?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is Gilbreath's Conjecture and Who's Researching It?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How are divisibility tests derived?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Need some advice for linear algebra
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Question about a Theorem in Gallian's Contemporary Abstract Algebra
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What is the flaw with this proof?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Proving Non-Isomorphism: Subgroup and Dihedral Group of Equal Order
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Understanding Homomorphisms: The Relationship Between A and B
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad How can changing the value of m affect the percentage p?
  • · Replies 7 ·
Replies
7
Views
4K
Graduate How to Find the Subgroup of a Quotient Group with a Given Generator?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Synthetic Division: Proving It Works
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Can a permutation with non-disjoint cycles still be used to find its order?
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Understanding Group Representations in Group Theory
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Learn Lie Groups & Lie Algebras with John Baez
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Linearly dependent set of vectors?
  • · Replies 6 ·
Replies
6
Views
9K
Graduate Isomorphism of A, B ∩ C: Techniques
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why is a homomorphism the way it is?
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Counting Subfields in F_p: Algebraic Result?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Proving Matrix X rank Decomposition
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What is the purpose of the transpose?
  • · Replies 5 ·
Replies
5
Views
29K
Graduate RQ decomposition from QR decomposition
  • · Replies 1 ·
Replies
1
Views
14K
Graduate What makes the Riemann Hypothesis so difficult to prove?
  • · Replies 17 ·
Replies
17
Views
5K
Graduate Proving that f(x) is Not Continuous for All Real Numbers c
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Modular Congruences of Integer Squares
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Matrix Exponentials: A, Eigenvalues, Jordan Form, Fundamental Matrix T
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Solving Diophantine Equations: Find Largest Number of Chicken Nuggets
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Solve Tennis Score Puzzle: Use Modular Arithmetic
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Prove Prime p^2+2 is Composite mod 3 #5
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Difference between R-algebra and R-module (R is a commutative ring)
  • · Replies 5 ·
Replies
5
Views
11K
Undergrad Rotation of Vector in P: Why Divide by r?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Does AB=G Imply AB=BA in Group Theory?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Number of distinct base
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Vector space of the product of two matrices
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Color theory:rgb to cmyk detailed mathematical description
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Real Numbers Vector Space: Countability of Basis
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Proof of Rational Root Theorem
  • · Replies 6 ·
Replies
6
Views
18K
Undergrad Practical applications of number theory?
  • · Replies 8 ·
Replies
8
Views
23K
Undergrad Is the Result of a Cross Product in R^3 a Vector in R^3?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Continued fractions and nested radicals
  • · Replies 5 ·
Replies
5
Views
8K
Graduate Determinant formula in monomials - can it be generalized?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Counting cycles in a permutation
  • · Replies 1 ·
Replies
1
Views
2K
High School How Can You Mentally Factor Numbers Without a Calculator?
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Group can be determined by how elements multiply with each other
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Can someone help me understand and evaluate the Riemann zeta function?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Recursive formula for zeta function of positive even integers
  • · Replies 8 ·
Replies
8
Views
9K
Finite Dimensional Vector Spaces - Paul R. Halmos
  • · Replies 8 ·
Replies
8
Views
12K
Graduate Isomorphic Groups: Same Info Studying 1 or Both
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Finding all vectors normal to a given set of vectors
  • · Replies 6 ·
Replies
6
Views
12K
High School Find Inverse of 2x2 Matrix: Step-by-Step Guide
  • · Replies 3 ·
Replies
3
Views
9K
Graduate C10 Group, 10th roots unity with complex number multiplication
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Three conjectures looking for a proof 100Euro reward
  • · Replies 9 ·
Replies
9
Views
3K
Graduate What is the intuition behind using eigenvectors of AA^T and A^T A in the SVD?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Efficient Computation of the Möbius Function
  • · Replies 3 ·
Replies
3
Views
6K
Graduate Why doesn't this presentation embed?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Connes Trace and Its Relation to Riemann Hypothesis: An Overview
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Odd Determinant: Explaining a Strange Phenomenon
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Normalizer of Sylow p-subgroup of simple groups A_n
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Need help proving Order of a formula
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Why the need for Lagrange's Theorem?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Solving Group G Show: Very Important!
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Solution for Polynomial Degree 7: x2=k2-k2x7/2
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Show G(p) of Order p^t when G is an Abelian Group of Order (p^t)m
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Quotienting is a generalisation of division
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Finding Solutions for a Matrix with Variables: Row Reduction Required?
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Linear Transformations and Dual Vectors: Understanding Matrix Representations
  • · Replies 4 ·
Replies
4
Views
4K