Linear and Abstract Algebra Forum

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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.
Can a Linear Transformation Satisfy One Property but Not the Other?
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MHB Matrix Exponential and series idenfication
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Having trouble understanding minimal polynomial problems
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A deeper understanding of the determinate
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Simple Proofs for Matrix Algebra Properties: A Beginner's Guide
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MHB Construct a matrix with such that V is not equal to C_x
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MHB Show deg of minimal poly = dimension of V
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MHB Tensor Products - Keith Conrad - Theorem 3.3 - Tensor Products I
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MHB Polynomial including Sigma Notation
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Calculating Basis of Tangent Plane
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MHB Existence of Tensor Products - Keith Conrad - Tensor Products I - Theorem 3.2
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Generating randomly oriented non-intersecting cylinders in a unit cell
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MHB Group Isomorphism: Proving G Is an Odd, Ablian Group
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MHB Difference Between Lines and Vectors (Linear Combination Problem)
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MHB What Are the Subgroups of Z_n When n Is Even?
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MHB Answer: Image Direct Sum & Linear Operator: Is Union Equal?
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Why f(x) = x^n - r e^{i \theta}? Seeking Analytic Explanation
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MHB Set of eigenvectors is linearly independent
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Number Theory: Why always elementary proofs?
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How Does the Adjoint Map Function in Lie Theory?
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MHB 3 Algebra problems that I with.
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MHB Introduction to Tensor Products - some advice please
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MHB Algorithm for finding all the borders of R in all dimensions?
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How Do You Sketch Re(iz) = 3 in Complex Number Plane?
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MHB Simple problem concerning R[x], R and a prime ideal I
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New irrational number to develop transcendental operators
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MHB Show that the matrix D is invertible
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Optimizing Vector Magnitude through 180-Degree Rotations
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MHB Localization - D&F Proposition 38., part (2)
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MHB Group of polynomials with coefficients from Z_10.
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MHB Solving a Matrix Equation: Choosing the Right Answer
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MHB Determine Sub-Vector Spaces of W & V
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Newton's expansion for non-commutative quantities
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Vector Formula with multiple Equal signs?
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MHB Which of the Following is Incorrect Regarding Matrices and Vectors?
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Approximate diagonalisation of (3,3) hermitian matrix
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MHB Localization - Bijections between prime ideals of R and D^-1R
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MHB Finding a positive definite matrix to satisfy the general equation of an ellipse
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Fully reducible rep-invariant subspace
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MHB Positive, definite matrix symmetric
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Understanding Solutions and Singular Matrices
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Pythagorean theorem based on cross product.
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MHB Free and Finitely Generated Modules
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Inner products and the dual space
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MHB Collection of Subspaces of a Vector Space
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Infinity and one norm question
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Understanding Linear Combinations of Vectors
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How Does Matrix Exponentiation Retrieve Rotation Matrices?
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When y is negative in linear regression?
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Algorithm for Generating Percentage Amounts
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Understanding the Com of a Matrix: Properties and Applications
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MHB Describe Geometrically (line, plane, or all of R3) all linear combinations of:
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MHB R-modules and Homomorphism of Rings
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MHB Localization - Dummit and Foote, EXAMPLE 2, Ch. 15, Section 15.4, page 708
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How can you manipulate a vector to create different matrices?
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Rotation Equations for 2 Angles: Combining Relationships for Easy Calculation
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Anthropomorphic Dummy Movements in 3D Space
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Transforming a spatial average into a spectral average
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Consistency of A System of Linear Equations
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MHB Localization in Commutative Ring Theory
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Scalar, vector and tensor calculus
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MHB If a row is added to any matrix is it still the same matrix?
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MHB Find Unit Vector Orthogonal to Vector
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Counterexample to Isomorphic Subfields: Help Needed
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What is the significance of the basis vector e_{11} in a bivector?
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How can I find a x such that the order of 2 mod x is n?
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Eigenvalues of two matrices are equal
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Covariant and Contravariant Coordinate
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How Does Tikhonov Regularization Handle Underflows in IEEE Double Precision?
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MHB Linear Function on a Vector Space
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MHB Self Adjoint and Unitary Transformations
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Why Is U(n) Considered Connected When O(n) Is Not?
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MHB Why Is There No Division for Vectors?
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MHB Linear Map Input: Solving P'(1-x) | \pi\rangle
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Cross product between unit vectos
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Finding the Intersection of a Line and Plane
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Why no general solution to quintic equations?
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MHB Extend to an orthonormal basis for R^3
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Rotational in terms of vector calculus
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MHB What Is the Relationship Between Radicals and Prime Ideals?
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Curl and divergence of units vectos
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MHB What Are Linear Transformations and How Do They Work?
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MHB Cauchy-Schwarz inequality for pre-inner product
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MHB Jordan Normal Form of a Linear Transformation
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Understanding Matrix Calculus: Laplacian, Hessian, and Jacobian Explained
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MHB Basis, dimension and vector spaces
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MHB Non-Singular Bilinear Function
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MHB Is the Space of Real Polynomials of Degree ≤ n a Euclidean Space?
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MHB Is the Lower Triangular Matrix in the Cholesky Decomposition Unique?
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Vector components and its coordinate description in a given basis
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MHB Ideals of a Residue Class Ring- Ring Isomorphism
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Question about normal subgroups/Lattice Isomorphism Theorem
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Irreducible representation. I'm confused.
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Quick question in linear algebra review for quantum mechanics
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Proving the special property of diagonal matrix?
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What does Z_2^5 mean in linear algebra notation?
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Consequence of the First isomorphism theorem
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Does Cayley's Theorem imply all groups are countable?
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Commutator of exponential operators
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What is the Relationship Between Position and Velocity Vectors?
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