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 Can You Help With Finite Element Analysis in Cylindrical Coordinates?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is Every Finite Complex Representation of a Compact Lie Group Unitary?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Finding elements in GL_2(R) with specific orders
  • · Replies 1 ·
Replies
1
Views
1K
MHB Prime Field of a Field k - Rotman Theorem 3.110
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solving Linear Equations: 2 Planes from LAX - Cbarker1
  • · Replies 1 ·
Replies
1
Views
2K
MHB Polynomial Rings _ Bland - Theorem 6.3.17
  • · Replies 8 ·
Replies
8
Views
2K
Graduate What is the difference between algebraic structure and space
  • · Replies 2 ·
Replies
2
Views
2K
MHB Polynomial Rings - Irreducibility
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Method to solve a coupled system of matrix equation
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Is it possible to find this number without brute force?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Why Do Functions \(X + UY\) and \(X - UY\) Have Zeroes Only at \(t = \pm 1\)?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Linear algebra and choosing training vector
  • · Replies 1 ·
Replies
1
Views
1K
MHB What Are the Solutions to the Equation \(x^2 + 2i = 0\)?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Why does $Y_n$ have that specific form?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Why is the set of cosines and sines a vector space?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Solving Vector Equation: Obtain m from F=ma
  • · Replies 7 ·
Replies
7
Views
2K
MHB Understanding the Equivalence in Diophantine Relations
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Proving Inverse Functions: Multiplicative Relationships
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Independent elements of matrices?
  • · Replies 6 ·
Replies
6
Views
5K
MHB Rational Functions - Polynomials Over a Field - Rotman Proposition 3.70
  • · Replies 11 ·
Replies
11
Views
3K
MHB UFDs .... Counterexample - I_8 = Z/8Z
  • · Replies 8 ·
Replies
8
Views
3K
MHB Polynomials Over a Field - Rotman, Lemma 3.87
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How can I use matrix algebra to rotate a polygon and calculate new coordinates?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Proof that all information can be coded in binary?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Not (null T) is a subspace of V?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Euclidean Rings - Rotman Example 3.76
  • · Replies 2 ·
Replies
2
Views
2K
MHB Properties of gcd's and relatively prime integers
  • · Replies 2 ·
Replies
2
Views
2K
MHB Polynomials Over a Field - Rotman, Lemma 3.67
  • · Replies 6 ·
Replies
6
Views
2K
MHB Why Is \(a\) a Unit in \(F[x]\) in Lemma 2 of Nicholson's Book?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Change of Basis, Covariant Vectors, and Contravariant Vector
  • · Replies 10 ·
Replies
10
Views
4K
MHB Factor Rings of Polynomials Over a Field - Nicholson, Lemma 1, Page 224
  • · Replies 7 ·
Replies
7
Views
2K
MHB Finding unknown coefficients to give a unique solution in a linear system
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad System of Linear Equations to Reduced Echelon Form
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Can Linear Programming Solve Problems with Division Constraints?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Are there other symmetries on the plane besides the wallpaper and point groups?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Equality of two elements of a hilbert space defined?
  • · Replies 11 ·
Replies
11
Views
2K
MHB How Does Nicholson Apply Induction in Theorem 12 Proof?
  • · Replies 4 ·
Replies
4
Views
3K
MHB Is {0} Considered the Smallest Integral Domain?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Scalar product and the Kronecker delta symbol
  • · Replies 4 ·
Replies
4
Views
2K
MHB Bilinear transformation not working
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Eigenvalues/eigenvectors using householder and QR
  • · Replies 5 ·
Replies
5
Views
5K
MHB What algebra rule is used here to give the exponent 2 in step 2?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Why Does \( p \) Divide \( f \) in Nicholson's Theorem 11?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Representation of Lorentz algebra
  • · Replies 1 ·
Replies
1
Views
1K
Graduate How Are Dual Vector Components Determined by Basis Vectors?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Interpreting U={A|A^2=A, A is in M22}: Not a Subspace of M22
  • · Replies 4 ·
Replies
4
Views
2K
MHB Factorization of Polynomials Over a Field - Nicholson Example 10, Page 215
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proving Vector Subspace $U \notin R^3$
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Asymmetry in MDS: Question on Unilateral Love & Hate
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How to Find the Basis of an Image
  • · Replies 6 ·
Replies
6
Views
7K
Undergrad Solve System of 4 Equations: Find x,y,u,v in Terms of a,b,c,d
  • · Replies 2 ·
Replies
2
Views
2K
MHB How can we show the other direction?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate On formal concept analysis (fca)
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad How can a 2D plane and 3D space accurately represent all colors?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Understanding: Eigenvalues & Eigenvectors/Diagonalizing
  • · Replies 7 ·
Replies
7
Views
2K
MHB Deriving Structure Factors for Lie Algebras | Dan's Project
  • · Replies 0 ·
Replies
0
Views
1K
MHB Proving $(x_n,y_n)$ Converge to $(20,20) for All $k$
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Does phrase «Space over vector field» make any sense?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Prove that a finite set with cancellation laws is a group
  • · Replies 9 ·
Replies
9
Views
7K
MHB Real Algebraic Curves: Solving Example 1.4 from C.G. Gibson's Book
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How does the cross product work?
  • · Replies 12 ·
Replies
12
Views
5K
MHB Solving a Polynomial Equation - Discussion in Fraleigh - Page 204
  • · Replies 1 ·
Replies
1
Views
1K
MHB Farmer Maths: Solving Optimal Number Problems with Matrix Maths
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Door Rotation Matrix/Change of Basis Plus Translation
  • · Replies 6 ·
Replies
6
Views
3K
MHB Affine Algebraic Curves - Kunz - Definition 1.1
  • · Replies 6 ·
Replies
6
Views
2K
MHB Kunz - Vanishing Ideal and Minimum Polynomial
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Do GCDs Coincide in Principal Ideals According to Rotman's Proposition 3.41?
  • · Replies 1 ·
Replies
1
Views
1K
MHB GCDs of Polynomials: Reading Rotman's Corollary 3.58
  • · Replies 1 ·
Replies
1
Views
1K
MHB Existential Theory: Understanding Last Proposition
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Vector coordinates and its points
  • · Replies 3 ·
Replies
3
Views
1K
MHB Find the value of k for the following system to have no solutions etc?
  • · Replies 2 ·
Replies
2
Views
1K
MHB How Can We Construct a Unique Linear System From Given Conditions?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Polynomials and Polynomial Functions in I_m = Z/mZ
  • · Replies 1 ·
Replies
1
Views
1K
MHB Ring Homomorphisms - Rotman - Theorem 3.33
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proof Noetherian Ring: $M^2 \ne M$
  • · Replies 3 ·
Replies
3
Views
2K
MHB Why Does Every Element in U(\mathbb{I}_m) Have an Inverse?
  • · Replies 7 ·
Replies
7
Views
3K
MHB Congruences - Rotman - Proposition 1.58
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad What is the relationship between the determinant and orientation in R^2?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Congruences - Rotman - Proposition 1.58 - Second Question
  • · Replies 1 ·
Replies
1
Views
1K
Graduate I'm stuck on a proof that's probably trivial, any insights?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Vandermonde Determinant, what am i doing wrong?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Product of exponential of operators
  • · Replies 1 ·
Replies
1
Views
6K
Undergrad What Are Examples of Non-Linear Operators in Mathematics?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Skew-symmetric matrix property
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Rotation matrix between two orthonormal frames
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Rewriting a constraint as a standard SOC constraint.
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Determining if logical matrix represents a partial order
  • · Replies 1 ·
Replies
1
Views
4K
MHB Universal Property for Coproducts in Ab
  • · Replies 4 ·
Replies
4
Views
2K
MHB Shankar - Simultaneous Diagonalisation of Hermitian Matrices
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Is conditional arrangement of cells in a mxn matrix unique?
  • · Replies 6 ·
Replies
6
Views
1K
MHB Find $\vec{AC}.\vec{AB}$ in Rectangle $ABCD$
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Proving uniqueness of a mathematical object
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Proving a linear algebra equation
  • · Replies 3 ·
Replies
3
Views
2K
MHB Calculating the effect of an operator on an arbitrary state
  • · Replies 5 ·
Replies
5
Views
2K
MHB Relation between matrix elements of momentum and position operators
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Underdetermined vs Overdetermined Systems
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Understanding Schwarz Inequality and Its Role in Higher Dimensions
  • · Replies 1 ·
Replies
1
Views
1K
MHB Ring Without Identity - (mZ, +, * )
  • · Replies 3 ·
Replies
3
Views
2K
MHB Initial Objects in the Category Ring
  • · Replies 4 ·
Replies
4
Views
2K