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SquareMatrixQ[m]

gives True if m is a square matrix, and False otherwise.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Special Matrices  
Applications  
Properties & Relations  
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SquareMatrixQ

SquareMatrixQ[m]

gives True if m is a square matrix, and False otherwise.

Details

  • A matrix m is square if it has the same number of rows and columns, in which case Dimensions[m]{n,n}. »
  • SquareMatrixQ works for symbolic as well as numerical matrices.

Examples

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Basic Examples  (3)

Test if an object is a square matrix:

Wolfram Language code: SquareMatrixQ[(⁠| | | | - | - | | 1 | 2 | | 3 | 4 |⁠)]

The following matrix is not square:

Wolfram Language code: SquareMatrixQ[(⁠| | | | | - | - | - | | 1 | 2 | 3 | | 4 | 5 | 6 |⁠)]

These are not matrices:

Wolfram Language code: SquareMatrixQ[{1, 2, 3}]
Wolfram Language code: SquareMatrixQ[{{1}, {2, 3}}]

Scope  (9)

Basic Uses  (5)

Test if a real machine-precision matrix is square:

Wolfram Language code: m = {{1.2, -2.3}, {2.6, 3.4}};
Wolfram Language code: SquareMatrixQ[m]

Test if a complex matrix is square:

Wolfram Language code: m = {{I, 2 - 3I}, {-2 - 3I, -I}};
Wolfram Language code: SquareMatrixQ[m]

Test if an exact matrix is square:

Wolfram Language code: m = (⁠| | | | | | -- | - | -- | -- | | 2 | 4 | -1 | -5 | | -5 | 1 | 3 | -3 | | -4 | 3 | -2 | 2 |⁠);
Wolfram Language code: SquareMatrixQ[m]

Make the matrix square:

Wolfram Language code: SquareMatrixQ[m.m^]

Use SquareMatrixQ with a symbolic matrix:

Wolfram Language code: SquareMatrixQ[{{a, b}, {c, d}}]

SquareMatrixQ works efficiently with large numerical matrices:

Wolfram Language code: m = RandomReal[1, RandomInteger[{1000, 2000}, 2]];
Wolfram Language code: AbsoluteTiming[SquareMatrixQ[m]]
Wolfram Language code: a = m.m^; AbsoluteTiming[SquareMatrixQ[a]]

Special Matrices  (4)

Use SquareMatrixQ with sparse matrices:

Wolfram Language code: SparseArray[{{1, 1} -> 1, {1, 2} -> 2, {2, 2} -> 3, {2, 1} -> 4}, {2, 2}]
Wolfram Language code: SquareMatrixQ[%]
Wolfram Language code: SparseArray[{i_, j_} -> i - j + (i + j)I, {5, 4}]
Wolfram Language code: SquareMatrixQ[%]

Use SquareMatrixQ with structured matrices:

Wolfram Language code: SymmetrizedArray[{{1, 2} -> 4, {3, 2} -> 5}, {3, 3}, Antisymmetric[All]]
Wolfram Language code: SquareMatrixQ[%]

Use with a QuantityArray structured matrix:

Wolfram Language code: QuantityArray[{{1, 2}, {2, 5}}, {"Meters", "Seconds"}]
Wolfram Language code: SquareMatrixQ[%]

Use SquareMatrixQ with an identity matrix:

Wolfram Language code: SquareMatrixQ[IdentityMatrix[5]]
Wolfram Language code: SquareMatrixQ[IdentityMatrix[{5, 3}]]

Use SquareMatrixQ with HilbertMatrix:

Wolfram Language code: SquareMatrixQ[HilbertMatrix[5]]
Wolfram Language code: SquareMatrixQ[HilbertMatrix[{5, 6}]]

Applications  (1)

Define a function that only evaluates for explicit square matrices:

Wolfram Language code: hpart[m_ ? SquareMatrixQ] := (m + ConjugateTranspose[m]) / 2

This represents the Hermitian part of a matrix explicitly:

Wolfram Language code: hpart[{{1, 2I}, {3I, 4}}]
Wolfram Language code: HermitianMatrixQ[%]

This does not evaluate because the matrix is rectangular:

Wolfram Language code: hpart[{{1, 2I, -3}, {3I, 4, 0}}]

This does not evaluate because a is not an explicit matrix:

Wolfram Language code: hpart[a]

Properties & Relations  (5)

For a square matrix m, Dimensions[m] gives {n,n}:

Wolfram Language code: Dimensions[(| | | | | - | - | - | | 1 | 2 | 3 | | 4 | 5 | 6 | | 7 | 8 | 9 |)]

SquareMatrixQ[expr] returns False for expressions that are not matrices:

Wolfram Language code: SquareMatrixQ["string"]
Wolfram Language code: SquareMatrixQ[1]

The empty list is not considered a square matrix:

Wolfram Language code: SquareMatrixQ[{}]

A square matrix is made up of vectors of length :

Wolfram Language code: m = RandomReal[1, {3, 3}];

Make sure it is made up of vectors:

Wolfram Language code: And@@Map[VectorQ, m]
Wolfram Language code: And@@Map[VectorQ, {}]

Verify that all vectors have the same length and the number of vectors equals their length:

Wolfram Language code: Equal@@Append[Map[Length, m], Length[m]]

Hence m is a square matrix:

Wolfram Language code: SquareMatrixQ[m]

For lists, SquareMatrixQ[a] is equivalent to MatchQ[TensorDimensions[a],{n,n}]:

Wolfram Language code: MatrixForm[m = RandomReal[1, RandomInteger[{2, 4}, {2}]]]
Wolfram Language code: SquareMatrixQ[m] == MatchQ[TensorDimensions[m], {n_, n_}]
Wolfram Research (2014), SquareMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SquareMatrixQ.html.

Text

Wolfram Research (2014), SquareMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SquareMatrixQ.html.

CMS

Wolfram Language. 2014. "SquareMatrixQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SquareMatrixQ.html.

APA

Wolfram Language. (2014). SquareMatrixQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SquareMatrixQ.html

BibTeX

@misc{reference.wolfram_2026_squarematrixq, author="Wolfram Research", title="{SquareMatrixQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SquareMatrixQ.html}", note=[Accessed: 15-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_squarematrixq, organization={Wolfram Research}, title={SquareMatrixQ}, year={2014}, url={https://reference.wolfram.com/language/ref/SquareMatrixQ.html}, note=[Accessed: 15-June-2026]}