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 Measuring Sequence Similarity with Absolute Differences
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Multidimensional cross product vector
  • · Replies 5 ·
Replies
5
Views
6K
Graduate Constructing a 2D Matrix for Solving Equations with Multiple Unknowns
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad No problem, glad I could help! Keep up the good work in your studies.
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Proof of R Transpose and Inverse Equals Identity Matrix
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How can the recurrence relations for Eisenstein series G_k(z) be proven?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Proof of the Cauchy Shwarz inequality
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Ideal/Submodule Query - Proving R is Principal Ideal Domain
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Discover the Cute and Simple Formula for Pi Derived from the Dirchlet Function
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Riemann hypothesis and number theory
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Understanding the Relationship Between Lie Algebras and Lie Groups
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Finding a smaller subset within a set
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Eigenvalues of sum of a Hermitian matrix and a diagonal matrix
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Find a basis for the space of 2x2 symmetric matrices
  • · Replies 2 ·
Replies
2
Views
14K
High School Inverse of b mod n: Find, Steps, Examples
  • · Replies 1 ·
Replies
1
Views
11K
Undergrad Solving Pell's Equation: I'm Stuck!
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Can Fractals Predict Prime Positions Through Partition Numbers?
  • · Replies 5 ·
Replies
5
Views
6K
Graduate Right handed frames and Orientation
  • · Replies 12 ·
Replies
12
Views
4K
Graduate Is the Tensor Product Associative?
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Fundamental theorem of Orthogonality
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad So, do negative prime numbers exist?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad I don't get Eigenvalues or Eigenvectors
  • · Replies 29 ·
Replies
29
Views
24K
Undergrad How Can You Roll a 13 Using 2 Dice?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Efficient Fortran Subroutines for Matrix Diagonalisation: Small Matrices
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Good luck!Proving the Relationship between Fibonacci and Lucas Series
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What Are the Key Concepts in Understanding Genus 2 Hyperelliptic Curves?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Proving the Sum of Hermitian Matrices is Hermitian
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is the Conjugate of a Polynomial the Same as Its Conjugate Field?
  • · Replies 6 ·
Replies
6
Views
9K
Graduate Is an un-spannable vector space automatically considered infinite dimensional?
  • · Replies 10 ·
Replies
10
Views
3K
Graduate What Is the P-adic Volume of the P-adic Circle x² + y² = 1?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Proof of an identity in determinants
  • · Replies 7 ·
Replies
7
Views
3K
Graduate A Surjective Function for All [R]
  • · Replies 11 ·
Replies
11
Views
5K
Graduate Hadamard product to Matrix product transformation
  • · Replies 3 ·
Replies
3
Views
15K
Graduate Is every element in F algebraic over Q?
  • · Replies 17 ·
Replies
17
Views
5K
Graduate |G|=4. Prove the group is either cyclic or g^2=e
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Is There a Connection Between Ken Ono and Factoring?
  • · Replies 6 ·
Replies
6
Views
5K
Graduate What do French, German, and Russian texts call the Cauchy-Schwarz inequality?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad How to scale an input number range ?
  • · Replies 2 ·
Replies
2
Views
5K
Graduate |G|=p^k. Prove G has an element of order p.
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Show K⊂R⊂F Fields: Algebraic Over K => R is a Field
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Number Theory Puzzler: Proving N-S is a Multiple of 9
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Proving the Number of Digits in a Number Formula: A Scientific Exploration
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad The units of a cartesian product?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Prove that G is a linear vector space
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Is f(x) Idempotent for Any Matrix B in M2(R)?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate What is the significance of k being a multiple of 2 or 3?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Is sqrt(5) Rational? Understanding the Proof by Contradiction
  • · Replies 60 ·
3
Replies
60
Views
61K
Graduate Diffrence between U(1) and Spin(1)?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Is this statement about the rank of a linear map true or false?
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad Matrix inverse equals power-series
  • · Replies 18 ·
Replies
18
Views
48K
Graduate How do you prove that the operations on cosets in rings are well-defined?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Relating Two Notions of Tensor Product
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Change of Basis + Geometric, Algebraic Multiplicities
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Harmonic series, slowest diverging series?
  • · Replies 4 ·
Replies
4
Views
8K
Undergrad Is matrixs multiplication random ?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Logical Systems+new Principles+attempt To Solve Collatz Conjecture
  • · Replies 5 ·
Replies
5
Views
5K
Graduate Tensor Rank of 2X2 Matrix: Is It Always 2?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Expected Value and covariance of matrix
  • · Replies 3 ·
Replies
3
Views
6K
Graduate What is the definition of affine n-space in algebraic geometry?
  • · Replies 6 ·
Replies
6
Views
6K
Graduate How Do I Prove Ring Properties and Understand Their Structures?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Why Define Inner Products for Complex Vector Spaces Using Complex Conjugation?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Euler's number e and Jacob Bernoulli's expression
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What Are All the Homomorphisms from Z to Z?
  • · Replies 9 ·
Replies
9
Views
27K
Undergrad Proof of Idempotent Matrix with Inverse = Identity Matrix
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Is it possible to generalize it?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate HELP Mathematical notation needed for a prime mod 12 pattern
  • · Replies 15 ·
Replies
15
Views
8K
Undergrad Why Do Physics & Engineering Tools Form Groups?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate How can I find the optimal vector x for a constrained optimization problem?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Simplifying Square Roots: Unraveling the Mystery of the Square Root Function
  • · Replies 15 ·
Replies
15
Views
8K
Graduate Derivative (mimization) of matrix trace
  • · Replies 5 ·
Replies
5
Views
6K
Graduate Finding coefficients using dual basis
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Motivating Matrix Addition/Multiplication Without Appealing to Linear Maps
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How to prove (p-1) = -1 (mod p), p is a prime.
  • · Replies 2 ·
Replies
2
Views
8K
Undergrad The largest number not in the form of ax+by, with gdc(a,b)=1.
  • · Replies 13 ·
Replies
13
Views
9K
Graduate Can a Vector Space Over Field F Contain Entries from Other Fields?
  • · Replies 10 ·
Replies
10
Views
5K
Graduate The geometric mutiplicity of a matrix
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Complex conjugation and vector space duality
  • · Replies 14 ·
Replies
14
Views
10K
Graduate Is an Ideal Always a Linear Space?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What is the intersection of nullspaces of S1, S2, and S3?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Square matrix with no eigenvectors?
  • · Replies 17 ·
Replies
17
Views
27K
Graduate To PI or not to PI challenge. Stern-Brocot
  • · Replies 28 ·
Replies
28
Views
9K
Graduate Why is Supremum of a.u Less Than or Equal to r||a||_2?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Green's Relations and Their Congruences
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Vector Space of Functions & Matrices: Notation Explained
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad 2*T_x + 1 is Triangular & 3*T_x + 1 is also Triangular
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Prove that any two elements of order 3 in GL(2,Z) are conjugates.
  • · Replies 2 ·
Replies
2
Views
3K
Graduate How can you determine if a composite extension is purely inseparable?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to count the total # of non-invertible 2x2 matrices
  • · Replies 7 ·
Replies
7
Views
7K
Undergrad (Not a Proof of) Goldbach's Conjecture
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad Is Determinant Multiplication Commutative and What Does |AB|=|BA| Imply?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Similarity transformation to the transpose
  • · Replies 8 ·
Replies
8
Views
8K
Graduate Breaking RSA if you know m^k = 1 mod n
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Collatz Conjecture Paper: Check it Out & Give Opinion
  • · Replies 9 ·
Replies
9
Views
5K
Graduate Why is it possible for 1 to equal 0 in a trivial ring?
  • · Replies 11 ·
Replies
11
Views
6K
Graduate Understanding TM* (tensorproduct) TM*: Let's Break it Down!
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Linear dependence of square matrices
  • · Replies 2 ·
Replies
2
Views
3K
Graduate How do I numerically compute a state-space equation?
  • · Replies 4 ·
Replies
4
Views
8K
Graduate Efficient Goldbach Partitions Formula with Intuitive Reasoning
  • · Replies 12 ·
Replies
12
Views
5K
Graduate Observation: A Prime / Mersenne / (Ramanujan) Triangular Number Convolution
  • · Replies 8 ·
Replies
8
Views
5K
High School Why were the Greek and Roman systems of numbers not used for actual calculation?
  • · Replies 2 ·
Replies
2
Views
5K