Simple question. Can one write every second rank tensor $T^{ab}$ as some finite sum $\sum U^aV^b$ with $U^a$, $V^b$ tensors? Apologies if this is an incredibly standard result - I don't own a textbook on tensors! If this indeed is true, then presumably it generalises to tensors of all ranks?
2026-02-23 13:06:10.1771851970
Relationship between Tensors of Different Rank
263 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in TENSORS
- Linear algebra - Property of an exterior form
- How to show that extension of linear connection commutes with contraction.
- tensor differential equation
- Decomposing an arbitrary rank tensor into components with symmetries
- What is this notation?
- Confusion about vector tensor dot product
- Generalization of chain rule to tensors
- Tensor rank as a first order formula
- $n$-dimensional quadratic equation $(Ax)x + Bx + c = 0$
- What's the best syntax for defining a matrix/tensor via its indices?
Related Questions in TENSOR-RANK
- Tensor rank as a first order formula
- 3+ Dimensional Matrices
- Manipulating tensor products
- Why are the covariant and contravariant components of the metric tensor defined this way?
- For all rank two tensors, is $A:BC = AB^T:C$?
- How to find eigenvalues and eigenvectors of higher-order tensors?
- tensor product, isotropic
- Uniqueness of Tensor Decompositions (Aren't Matrix Decompositions a Special Case?)
- Actual example of tensor contraction
- Could a Rank Two Tensor be a Scalar?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?