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 Solution space to homogenous equations.
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How to Find the General Solution for a Matrix with a Free Variable?
  • · Replies 6 ·
Replies
6
Views
9K
Undergrad Simple intuitive/graphical interpretation of the Gauss-Seidel method
  • · Replies 8 ·
Replies
8
Views
6K
Graduate Vector Space, dimensions and kernal rank
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Eigenvectors of commuting matrices
  • · Replies 5 ·
Replies
5
Views
11K
Graduate Group Action on Set S: The Induced Homomorphism from g \in S_{5}
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Theorem concerning free abelian groups
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Module action sends zero to zero?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Can You Decrypt This Encrypted Text Using a Numerical Technique?
  • · Replies 39 ·
2
Replies
39
Views
9K
Graduate Number of invertible/non-singular matrices over a finite field
  • · Replies 2 ·
Replies
2
Views
11K
Graduate Isomorphism beetwenn vector space and sub space
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Stronger Goldbach-related conjecture
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Triangular Form for Linear Transformations: Finding Basis for Null Spaces
  • · Replies 3 ·
Replies
3
Views
9K
Undergrad Why Did People Accept Imaginary Numbers Before Negative Numbers?
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Very very quick quiestion about D_4?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate How Many Quadratic Forms Exist on Fp^n for an Odd Prime p?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is There a More Efficient Way to Prove a Homomorphism in Z_10->Z_10?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Knot Invariants and Related Topics - Tips for Learning
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Prove quotient ring of PID is PID too
  • · Replies 5 ·
Replies
5
Views
9K
Graduate Primitive Matrix: Is M^k Positive?
  • · Replies 1 ·
Replies
1
Views
7K
Undergrad Linear programming and the two phase method
  • · Replies 2 ·
Replies
2
Views
22K
Undergrad Discovering the Image of a Linear Map: Methods and Examples
  • · Replies 5 ·
Replies
5
Views
6K
Graduate Solubility of the General Linear Group
  • · Replies 2 ·
Replies
2
Views
2K
High School Does .999~=1? A Beginner's Perspective
  • · Replies 57 ·
2
Replies
57
Views
15K
Graduate Approximate finding nearest neighbor vectors
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Any implications of this diagonal element inequality?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Can You Find a Matrix Where Column Space Equals Null Space?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Prime Numbers in Cryptography: Uses & Benefits
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Mapping ( linear transformation)
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Proving the Converse: Finite Field with Cyclic Group of Units
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Proving Inequalities Involving Vector Space Dimensions
  • · Replies 3 ·
Replies
3
Views
3K
Graduate What Does Closed Mean in the Context of Lie Subgroups?
  • · Replies 26 ·
Replies
26
Views
7K
Graduate Order of groups in relation to the First Isomorphism Theorem.
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Proving the Properties of Pseudo Inverse and Transpose
  • · Replies 2 ·
Replies
2
Views
7K
Graduate Generator of the additive gr. Z_m
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Please explain the different morphisms to me
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Generalized Cartan Matrix and Non-Semisimple Lie Algebras
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Can singular value decomposition be used for complex matrices?
  • · Replies 1 ·
Replies
1
Views
9K
Graduate Isomorphisms between cyclic groups
  • · Replies 4 ·
Replies
4
Views
7K
Graduate Proving the Relationship Between Perfect Numbers and Harmonic Mean
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Solving Linear Congruence: 12x \equiv 1(mod5)
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Abstract Algebra Struggles: Navigating Levi and Malcev Theorems
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Any finite group has an even number of elements
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How Do Continuous Linear Representations of S^1 Function in Hilbert Spaces?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Find Product Identity with ABCD & Triangular Variables
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Can you find the least-squares solution and projection of this matrix equation?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Precise definition of linear combination
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Can You Identify 10 Non-Isomorphic Groups with Orders 25-29?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Find Quadratic Numbers in Z3 - Marin's Help Request
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Matrix Identify involving Diagonal Matrix
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Asking for Linear programming problems
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Vacuous truth in regards to vector spaces
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Is every Toeplitz matrix invertible?
  • · Replies 2 ·
Replies
2
Views
6K
Graduate What are the best resources for understanding Jordan Canonical Form proofs?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Why Are Half of the Permutations in Sn Even and the Other Half Odd?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What is the Wedge Product in Theoretical Physics?
  • · Replies 5 ·
Replies
5
Views
8K
Undergrad Find Eigen Values: Solve Char. Equation |A-#I| = 0 of Degree 3
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Have you encountered this famous matrix before?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is Every Prime > 3 a Sum of a Prime and a Power of Two?
  • · Replies 93 ·
4
Replies
93
Views
17K
Undergrad How Many Ways Can a Natural Number M Be Expressed as a Sum of N Whole Numbers?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Scalar triple product, volume, and ordering
  • · Replies 7 ·
Replies
7
Views
10K
Undergrad Equation of a plane (General and Point-Normal Form)
  • · Replies 19 ·
Replies
19
Views
26K
Graduate Prime Number Theorem: Proving Equivalence of $P(x)$ and $Li(x)$
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Divisibility and Congruence problem
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Are there any other twin primes with this property?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Determining Normal Subgroups in S(3) - A Mathematical Puzzle
  • · Replies 8 ·
Replies
8
Views
3K
High School Solve Equation Problem: 5x+6y=40 - Help & Hints
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Solving vv^T = M: Solve Unknown Vector & Matrix Equation
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad When to us dot versus cross product
  • · Replies 2 ·
Replies
2
Views
2K
High School Are two vectors with opposite angles parallel to each other?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad What Does the Mathematical Operation f:S --> R Mean?
  • · Replies 5 ·
Replies
5
Views
2K
High School Understanding Matrix Transpose and Examples | Learn about Matrix Transpose
  • · Replies 1 ·
Replies
1
Views
10K
Graduate How Can I Simplify This Linear Algebra Expression for Differentiation?
  • · Replies 15 ·
Replies
15
Views
5K
Graduate How to Simplify the Term for a Group Exercise?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Is integration of polynomial a bilinear for
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Computing Quotient Space: Practical Example with Vector Spaces and Subspaces
  • · Replies 2 ·
Replies
2
Views
9K
Undergrad Which algebraic rules altered for complex numbers?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Exponential sums and congruences
  • · Replies 5 ·
Replies
5
Views
3K
Graduate How Does the Infinite Sum of 1/j! Equal e?
  • · Replies 12 ·
Replies
12
Views
29K
Undergrad Distance between point-plane & plane-plane
  • · Replies 6 ·
Replies
6
Views
59K
Graduate Number Theory: Wilson's Theorem
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Order of an element in relation to the centre.
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Adjacent Transpositions of Permutations.
  • · Replies 6 ·
Replies
6
Views
13K
Graduate What is the most beautiful definition you've encountered?
  • · Replies 42 ·
2
Replies
42
Views
9K
Undergrad What is the algorithm for generating numbers based on a given input?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad What prerequisites are needed for studying linear algebra?
  • · Replies 3 ·
Replies
3
Views
21K
Graduate Orders of products of group elements.
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Is There a Way to Regularize Euler Products on Primes?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Number Theory Advice: Struggling with Proofs in Course
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Where is the flaw in this proof?
  • · Replies 13 ·
Replies
13
Views
4K
Graduate How can we parametrize a surface with an angle and radius?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Prove: X Contains at Most n(n-1)/2 Elements in Subset of a Group
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Determining whether homomorphism or not
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Proving Normalcy of H in Finite Group G
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Vector Subspace or Linear Manifold.
  • · Replies 13 ·
Replies
13
Views
15K
Undergrad Recommend a good Linear algebra text.
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Linear operator decomposition
  • · Replies 14 ·
Replies
14
Views
4K
High School What is the Hermitian Conjugate of 5+6i?
  • · Replies 3 ·
Replies
3
Views
6K
Graduate Exploring the Light Cone in Big Bang Clock by Roger Penrose
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Basis Vector Length: Unit Length & Mistakes to Avoid
  • · Replies 14 ·
Replies
14
Views
6K