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  (1)

Rank of an array:

Rank of a tensor product of two tensors:

Rank of a contraction:

Scope  (3)

Rank or depth of explicit arrays:

Rank of symbolic arrays:

Rank of general tensor expressions:

Options  (1)

Assumptions  (1)

Specify locally the domain of a symbolic array:

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:

This alternative construction would check for dimensions homogeneity:

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

Text

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

CMS

Wolfram Language. 2012. "TensorRank." Wolfram Language & System Documentation Center. Wolfram Research. 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_2023_tensorrank, author="Wolfram Research", title="{TensorRank}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/TensorRank.html}", note=[Accessed: 10-December-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_tensorrank, organization={Wolfram Research}, title={TensorRank}, year={2012}, url={https://reference.wolfram.com/language/ref/TensorRank.html}, note=[Accessed: 10-December-2023 ]}