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.
MHB The Significance of Row Space in a Matrix
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Can a vector be a linear combination of itself?
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Relative Prime Gaps: Fast Algorithm for Calc.
  • · Replies 13 ·
Replies
13
Views
5K
Graduate How to Find c in a Complex Logarithmic Equation?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Conjecture regarding perfect numbers.
  • · Replies 10 ·
Replies
10
Views
5K
Graduate Question regarding imaginary numbers and euler's formula
  • · Replies 9 ·
Replies
9
Views
4K
Graduate How Can We Understand Reflective Symmetry in a Square?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Understanding Matrix Row Spaces: Why It Matters
  • · Replies 2 ·
Replies
2
Views
2K
Graduate One-parameter group of transformations
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Eigenvectors of a symmetric matrix.
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Are Non-Singular Column Vectors of X Linearly Independent?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate What Is the Mathematical Depth Behind Ramanujan's Integral Identity?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Question on conditions for commutativity of subgroups
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad EASY QUESTION solving system of linear inequalities
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Are A, B, and A+B Always Coplanar?
  • · Replies 3 ·
Replies
3
Views
6K
Graduate Can Commutation between Subgroups be Achieved without Assuming Normality?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Solving the Clever Compound Cartoon Puzzle
  • · Replies 3 ·
Replies
3
Views
3K
MHB Solving System of Equations: Find # Solutions for Different Values of k
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Any useful analog to finite differences for matrix products?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate What Are Hamel & Schauder Bases and How Do They Relate to Vector Spaces?
  • · Replies 13 ·
Replies
13
Views
11K
Graduate Kronecker product of infinite dimensional matrices
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Homomorphism as a Structure-preserving Map.
  • · Replies 22 ·
Replies
22
Views
5K
Graduate Converting Rotation matrix to operate on fractional coordinates
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What is the Rank of the Adjugate Matrix?
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Can a Non-Linear Map be the Inverse of a Linear Map?
  • · Replies 8 ·
Replies
8
Views
3K
High School What Is an Efficient Way to Identify Composite Numbers?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate For which primes P is the following true?
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Checking if a Graph is Planar - v, e & f
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Possible Triplets for (1+1/a)(1+1/b)(1+1/c)=3
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solving a Coal Blending Problem with LP
  • · Replies 10 ·
Replies
10
Views
3K
MHB Is $f$ a function or a functional?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Question on Fermat's Last Theorem
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Understanding Group Structures: A Scientist's Perspective
  • · Replies 7 ·
Replies
7
Views
6K
Undergrad Can someone explain zeros and zeta function for Riemann Hypothesis? (Yr13)
  • · Replies 19 ·
Replies
19
Views
12K
Graduate Isomorphism of P4 and R5 in a given inner product space
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How Does Google Work? Get Answers Here
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How does the author determine the elements of order p or 4 in the group?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Understanding the Permitted Use of Double Summation in Math
  • · Replies 2 ·
Replies
2
Views
2K
High School What is the difference between zero scalar and zero vector?
  • · Replies 3 ·
Replies
3
Views
13K
Graduate Quick question about Hermitian operators
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Abelian groups and exponent of a group
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Proving/Disproving: Coprimes & (an + bn + cn ) / abc
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How do I solve a transcendental equation?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Question on definition of Lie groups
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Question about wiki artical on Quotient Groups
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Are there any real life applications of the rank of a matrix? It need
  • · Replies 3 ·
Replies
3
Views
9K
MHB Matrix Rank: Real-Life Applications & Motivation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How Does a Minimal Polynomial Differ from a Characteristic Polynomial?
  • · Replies 2 ·
Replies
2
Views
2K
High School Solving for Data: Formula with OUTPUT Provided
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Can anyone me to generalize and prove this if it is valid?
  • · Replies 5 ·
Replies
5
Views
6K
Undergrad Can you do the Cross Product Backwards?
  • · Replies 5 ·
Replies
5
Views
9K
High School Algebra - Associativity and Commutativity
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Where did this equation come from?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Number theory divisibility question
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Linear Functionals & Inner Products: Is This Theorem True?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Why Use A and B in Partial Fraction Decomposition?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad More than one identity element for absolute value?
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad What is eigen value, eigen vector etc and what is their physical significance?
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Determinants of matrices greater than 3x3
  • · Replies 6 ·
Replies
6
Views
8K
Undergrad Why Does Cramer's Rule Give Different Determinants for the Same Matrix?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Interpretation of the determinant of an operator in complex vector space
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Matrix Derivation: 2x1 A and B with Dimension and dA/dB Calculation
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad What are some real-life applications of general vector spaces?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Find Eigenvalues/Determinant of Infinite Matrix
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Direction of Goldbach Partitions
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad What is the determinant of a matrix?
  • · Replies 11 ·
Replies
11
Views
5K
Graduate Understanding Vector Spaces in Real Analysis
  • · Replies 5 ·
Replies
5
Views
3K
MHB Covariant and Contravariant Vector
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Finding all combination of portions of a number.
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Quick question about Linear Transformations from a space to itself
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Which Mathematician's Theorem Linked Prime Numbers to Cryptography?
  • · Replies 4 ·
Replies
4
Views
5K
MHB Showing that Q(sqrt(p)) is in Q adjoined the pth root of unity
  • · Replies 1 ·
Replies
1
Views
3K
MHB "structure" on the cosets → normal?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How to find 'self locating digits' in irrational numbers
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Must the Fourier transform exist for Dirac delta functions?
  • · Replies 6 ·
Replies
6
Views
4K
MHB Show that the abelian groups are isomorphic
  • · Replies 1 ·
Replies
1
Views
2K
High School Math Education: Encouraging Mediocrity and the Negative Effects of Algebra
  • · Replies 105 ·
4
Replies
105
Views
11K
High School What are the applications of permutations of a finite set?
  • · Replies 3 ·
Replies
3
Views
3K
MHB Generating a linear equation from the given expression
  • · Replies 5 ·
Replies
5
Views
2K
MHB Linear algebra. Rank. linear independence.
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Conjecture Regarding rotation of a set by a sequence of rational angles.
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is a Module? Polynomials & Vector Spaces
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Linear transformation and matrix transformation
  • · Replies 5 ·
Replies
5
Views
18K
Graduate Looking for Properties of Low Discrepancy Sequences.
  • · Replies 3 ·
Replies
3
Views
3K
Graduate 4th and higher dimension perpendicular
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Finding Inverse from Known Linear System
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Linearly independent eigen vectors
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Is Q-P Symmetric Positive-Definite?
  • · Replies 3 ·
Replies
3
Views
7K
MHB Introducing General Vector Spaces: Engaging Examples and Real-Life Applications
  • · Replies 2 ·
Replies
2
Views
3K
MHB Solve *-Algebra Problem: $\sigma(\lambda{e}-x)=\lambda-\sigma(x)$
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is this a complete test to show that a matrix is orthogonal?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Negative determinants when calculating eigenvectors?
  • · Replies 13 ·
Replies
13
Views
6K
Undergrad Decomposition of a Rotation Matrix
  • · Replies 7 ·
Replies
7
Views
9K
MHB How Do You Identify Scalar Homomorphisms in a Matrix Algebra?
  • · Replies 9 ·
Replies
9
Views
4K
High School Finding a formula for a sequence with recurring digits
  • · Replies 10 ·
Replies
10
Views
3K
Graduate What is the suitable representation of a linear operator of matrices?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Question on reducing 3 equations with 3 unknowns
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Equidistribution of points on a sphere
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Finding A in Non-Square Matrices: Pseudo Inverse vs Gradient Search
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Is There a Recognizable Pattern in the Distribution of Prime Numbers?
  • · Replies 20 ·
Replies
20
Views
6K