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.
Graduate How Does Graduate Math Differ from Undergraduate Algebra?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How can you simplify the quadratic formula using completing the square?
  • · Replies 282 ·
10
Replies
282
Views
49K
High School A logical (and simple) explanation for (-1*1=-1)?
  • · Replies 10 ·
Replies
10
Views
5K
Undergrad How to define the new vector in my case?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understanding the Confusion: Tensor Product vs. Dyadic Product for Vectors
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad Would does it mean to say that two matrices or functions are
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Properties of the super-golden ratio?
  • · Replies 5 ·
Replies
5
Views
11K
Graduate What Is the Physical Significance of the Norm of a Function in a Vector Space?
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Eigenvalues and eigenvectors of a matrix
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Integral of the reflection operator in arbitrary symmetric spaces.
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why Are 10-adics Not a Field?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Physics of Roulette: Spin, Friction, Wind, Momentum, Bounce
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What Does the Homomorphism from Z[x] to Z[i] Reveal About Its Ideals?
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad What is positive and negative eigenspaces? Can you recommend me a
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Prove a=0 for Ring Theory Question with m,n Positive Ints
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why E's representation marix is unit matrix
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Collatz Conjecture - Bouncing Ideas
  • · Replies 2 ·
Replies
2
Views
5K
Graduate What is the solvability condition for the matrix equation A_1x_2 = A_2x_1?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Powers of a superdiagonal matrix
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Understanding the Linearity Test for Inner Products
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Where are the irrational numbers?
  • · Replies 124 ·
5
Replies
124
Views
29K
Undergrad Goldbach's Conjecture (Theorem?)
  • · Replies 38 ·
2
Replies
38
Views
16K
Undergrad Is the column space of a matrix always a full span in practice?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Director product expansion of Lie groups.
  • · Replies 8 ·
Replies
8
Views
5K
Graduate Is Group Decomposition Unique in Semidirect Products?
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Matrix Dot Product: Solving Linear Algebra
  • · Replies 6 ·
Replies
6
Views
5K
Graduate How Does the Cyclic Decomposition Theorem Simplify Matrix Analysis?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Question about projections and subspaces
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Classic problems about parity property
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Determinant Identity for A-B and B A Matrices
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Can a Singular Matrix Always Find a Partner Matrix to Result in Zero?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Groups of order 21 (Need help understanding an inference)
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What puts the analysis in analytic number theory?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad A question about fourier analysis
  • · Replies 5 ·
Replies
5
Views
2K
Graduate At what point do the sums of the reciprocals converge?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Debating the Validity of the Inscribed Hexagon Theorem
  • · Replies 5 ·
Replies
5
Views
2K
Graduate What Is the Multilinear Eigenvalue Problem Called?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Group Homomorphism: Definition & Examples
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Finding Solutions for x12+x22=1 on Finite Fields Zp using Prime Number Algorithm
  • · Replies 4 ·
Replies
4
Views
7K
Graduate Reconsidering Pi: Examining the Controversy Surrounding its Accuracy
  • · Replies 57 ·
2
Replies
57
Views
11K
Graduate What is the Relationship Between Vectors and Newton's Second Law?
  • · Replies 10 ·
Replies
10
Views
5K
Graduate How do primes come out of Peano arithmetic?
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Tensor transformations for change of coordinate system
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Is There a Limit to the Number of Elements in a Coproduct/Direct Sum?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Why the roots of Eq. x^2 + a*x + b = 0 and of Eq. x + a*Sqrt[x] + b =
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Group Isomorphism: Proving f: Us(st)->U(t) is Onto
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Minimum Absolute Value of a nxn Matrix Determinant
  • · Replies 4 ·
Replies
4
Views
3K
High School Solve Tricky Sequence: 1,2,3,4,5,8,7,16,9
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Proving a set of derivatives to be a subset of real functions
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Shortcut method for order 4 and above.
  • · Replies 4 ·
Replies
4
Views
7K
Undergrad An efficient way to find perfect squares?
  • · Replies 15 ·
Replies
15
Views
9K
Undergrad Proving a set to be a vector space,
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Determining the Number of Invertible Elements in Zn
  • · Replies 13 ·
Replies
13
Views
13K
Graduate Is Every Complex Matrix Similar to Its Transpose?
  • · Replies 2 ·
Replies
2
Views
8K
Undergrad Galois Theory Intro Cut Short - Seeking Resources
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad True or false eigenvalue problem
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Bilinear Forms associated With a Quadratic Form over Z/2
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Solution to System with Unknown Variables n > 4
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How can I find a basis for the span of some eigenvectors?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Condition number of a matrix is 1 but determinant is almost 0
  • · Replies 2 ·
Replies
2
Views
9K
Graduate Counting continued fraction numbers
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Grothendieck decompostion simple example
  • · Replies 1 ·
Replies
1
Views
3K
Graduate External direct product- homomorphism
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Additive Prime Numbers: Is There Anything Known About them?
  • · Replies 2 ·
Replies
2
Views
7K
Undergrad Can't get my head into vector spaces and subspaces
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Nonzero R-Module over commuttaive ring, all submodules free => R PID?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Why Is Proving the Infinity of Fibonacci Primes So Challenging?
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad Proof of the Possibility of Division
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Rings as Algebras: Definitions & Questions
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Wiles Proof of Fermat's Last Theorem
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Understanding Graham's Number: A Comprehensive Guide
  • · Replies 5 ·
Replies
5
Views
10K
Graduate Ellipsoid algebra: converting forms
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Spherical Vector Addition Process
  • · Replies 3 ·
Replies
3
Views
9K
Graduate Can Least Squares be Applied to Matrices for Solving a Complex Equation?
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Notation in linear algebra and rule for square of matrix norm
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Number Theory, Linear & Abstract Algebra
  • · Replies 13 ·
Replies
13
Views
5K
Graduate Finite-Index Subgroups of Infinite Groups.
  • · Replies 8 ·
Replies
8
Views
6K
Graduate Confused about the concepts of dual spaces, dual bases, reflexivity and annihilators
  • · Replies 32 ·
2
Replies
32
Views
22K
Graduate Question on maximal ideals in an integral domain
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Why cant i learn linear algebra?
  • · Replies 11 ·
Replies
11
Views
8K
High School Why do vector multiplications result in different types of quantities?
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Difficult linear algebra problem
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Composition of permutation cycles
  • · Replies 1 ·
Replies
1
Views
3K
Graduate |a+b| = |a| + |b| implies a and b parallel?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How can a column vector be transformed into a diagonal matrix?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Finding rotation matrix with given new and old frame
  • · Replies 3 ·
Replies
3
Views
7K
Graduate Understanding Tensors: Comparing gαβAβ and Aβgαβ
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Examining the Taylor Series - Confused?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Dirichlet's Theorem on Arithmetic Progressions
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Why is the number of fixed points divisible by p in Cauchy's Theorem proof?
  • · Replies 4 ·
Replies
4
Views
5K
Graduate If x and y are parallel, then ha = b?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Matrix Multiplication and Rank of Matrix
  • · Replies 2 ·
Replies
2
Views
8K
Undergrad Modern Algebra & Real Analysis: Learn Proofwriting?
  • · Replies 9 ·
Replies
9
Views
5K
Graduate Finding Area Under a Helix: A Stumper Problem
  • · Replies 8 ·
Replies
8
Views
12K
Graduate The proof that an odd perfect number does not exist
  • · Replies 6 ·
Replies
6
Views
11K
Graduate Matrix multiplication preserve order Block matrix
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Existence of Roots for Quadratic Forms Modulo Prime Numbers
  • · Replies 9 ·
Replies
9
Views
5K
Graduate Orthogonal Basis in 3d is flipping.
  • · Replies 14 ·
Replies
14
Views
4K
Graduate What is the Connection Between Rank and Free Modules?
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Proving LCM Formula and GCD for Non-Integers
  • · Replies 59 ·
2
Replies
59
Views
14K