TensorRank

TensorRank[tensor]

gives the rank of tensor.

Details and Options

  • TensorRank accepts any type of tensor, either symbolic or explicit, including any type of array.
  • On explicit rectangular arrays of scalars, TensorRank coincides with ArrayDepth. On symbolic arrays, TensorRank stays unevaluated unless the array has been assigned a rank through any form of assumption.

Examples

open allclose all

Basic Examples  (4)

Rank of an array:

Rank of an array symbol:

Rank of a tensor product of two tensors:

Rank of a contraction:

Scope  (4)

Rank or depth of explicit arrays:

Rank of symbolic arrays:

Rank of vector, matrix, and array symbols:

Rank of general tensor expressions:

Options  (2)

Assumptions  (1)

Specify locally the domain of a symbolic array:

GenerateConditions  (1)

By default, TensorRank quietly makes assumptions necessary for the input to be well-defined:

With GenerateConditionsTrue, TensorRank gives a conditional result:

With GenerateConditionsNone, TensorRank fails when assumptions are necessary:

Properties & Relations  (2)

On explicit arrays, TensorRank coincides with ArrayDepth:

For symbolic expressions, there is no default rank assumed:

Use assumptions to assign a rank to the array:

Possible Issues  (3)

TensorRank can obtain some information contextually. Expressions without tensor properties inside numeric functions, arrays, or derivatives are considered scalars:

It is not possible to mix incompatible local and global assumptions:

TensorRank does not check for dimensions homogeneity, only rank homogeneity:

With GenerateConditionsTrue, TensorRank checks for dimensions homogeneity:

Wolfram Research (2012), TensorRank, Wolfram Language function, https://reference.wolfram.com/language/ref/TensorRank.html (updated 2024).

Text

Wolfram Research (2012), TensorRank, Wolfram Language function, https://reference.wolfram.com/language/ref/TensorRank.html (updated 2024).

CMS

Wolfram Language. 2012. "TensorRank." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/TensorRank.html.

APA

Wolfram Language. (2012). TensorRank. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TensorRank.html

BibTeX

@misc{reference.wolfram_2025_tensorrank, author="Wolfram Research", title="{TensorRank}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TensorRank.html}", note=[Accessed: 05-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_tensorrank, organization={Wolfram Research}, title={TensorRank}, year={2024}, url={https://reference.wolfram.com/language/ref/TensorRank.html}, note=[Accessed: 05-May-2025 ]}