Antisymmetry of a Matrix code-golf matrix

A matrix is antisymmetric, or skew-symmetric, if its transpose equals its negative.

The transpose of a matrix can be obtained by reflecting its elements across the main diagonal. Examples of transpositions can be seen here:

\$\begin{pmatrix}11&12&13\\21&22&23\end{pmatrix}\rightarrow\begin{pmatrix}11&21\\12&22\\13&23\end{pmatrix}\$

\$\begin{pmatrix}11&12&13\\21&22&23\\31&32&33\end{pmatrix}\rightarrow\begin{pmatrix}11&21&31\\12&22&32\\13&23&33\end{pmatrix}\$

This matrix is antisymmetric because it equals its transpose when multiplied by -1:

\$\begin{pmatrix}0&2&-1\\-2&0&0\\1&0&0\end{pmatrix}\$

All antisymmetric matrices exhibit certain characteristics:

• Antisymmetry can only be found on square matrices, because otherwise the matrix and its transpose would be of different dimensions.

• Elements which lie on the main diagonal must equal zero because they do not move and consequently must be their own negatives, and zero is the only number which satisfies \$x=-x\$.

• The sum of two antisymmetric matrices is also antisymmetric.

The Challenge

Given a square, non-empty matrix, check whether it is antisymmetric or not.

Rules

• This is code-golf so the shortest program in bytes wins.

• Input and output can assume whatever forms are most convenient.

• Assume only valid input will be given.

Test Cases

In: 1 1 1 1 1 1 1 1 1 Out: False In: 0 0 1 0 0 0 -1 0 0 Out: True In: 0 -2 2 0 Out: True 

Posted: Antisymmetry of a Matrix

Antisymmetry of a Matrix code-golf matrix

A matrix is antisymmetric, or skew-symmetric, if its transpose equals its negative.

The transpose of a matrix can be obtained by reflecting its elements across the main diagonal. Examples of transpositions can be seen here:

\$\begin{pmatrix}11&12&13\\21&22&23\end{pmatrix}\rightarrow\begin{pmatrix}11&21\\12&22\\13&23\end{pmatrix}\$

\$\begin{pmatrix}11&12&13\\21&22&23\\31&32&33\end{pmatrix}\rightarrow\begin{pmatrix}11&21&31\\12&22&32\\13&23&33\end{pmatrix}\$

The following matrix is antisymmetric, because it equals its transpose when multiplied by -1:

\$\begin{pmatrix}0&2&-1\\-2&0&0\\1&0&0\end{pmatrix}\$

All antisymmetric matrices exhibit certain characteristics. Antisymmetry can only be found on square matrices, because otherwise the matrix and its transpose would be of different dimensions. Additionally, elements which lie on the main diagonal must equal zero because they do not move and consequently must equal their negative, and zero is the only number which satisfies \$x=-x\$.

The Challenge

Given a square, non-empty matrix, check whether it is antisymmetric or not.

Rules

• This is code-golf so the shortest program in bytes wins.

• Input and output can assume whatever forms are most convenient.

• Assume only valid input will be given.

Test Cases

In: 1 1 1 1 1 1 1 1 1 Out: False In: 0 0 1 0 0 0 -1 0 0 Out: True In: 0 -2 2 0 Out: True 

Antisymmetry of a Matrix code-golf matrix

A matrix is antisymmetric, or skew-symmetric, if its transpose equals its negative.

The transpose of a matrix can be obtained by reflecting its elements across the main diagonal. Examples of transpositions can be seen here:

\$\begin{pmatrix}11&12&13\\21&22&23\end{pmatrix}\rightarrow\begin{pmatrix}11&21\\12&22\\13&23\end{pmatrix}\$

\$\begin{pmatrix}11&12&13\\21&22&23\\31&32&33\end{pmatrix}\rightarrow\begin{pmatrix}11&21&31\\12&22&32\\13&23&33\end{pmatrix}\$

This matrix is antisymmetric because it equals its transpose when multiplied by -1:

\$\begin{pmatrix}0&2&-1\\-2&0&0\\1&0&0\end{pmatrix}\$

All antisymmetric matrices exhibit certain characteristics:

• Antisymmetry can only be found on square matrices, because otherwise the matrix and its transpose would be of different dimensions.

• Elements which lie on the main diagonal must equal zero because they do not move and consequently must be their own negatives, and zero is the only number which satisfies \$x=-x\$.

• The sum of two antisymmetric matrices is also antisymmetric.

The Challenge

Given a square, non-empty matrix, check whether it is antisymmetric or not.

Rules

• This is code-golf so the shortest program in bytes wins.

• Input and output can assume whatever forms are most convenient.

• Assume only valid input will be given.

Test Cases

In: 1 1 1 1 1 1 1 1 1 Out: False In: 0 0 1 0 0 0 -1 0 0 Out: True In: 0 -2 2 0 Out: True 

Antisymmetry of a Matrix code-golf matrix

A matrix is antisymmetric, or skew-symmetric, if its transpose equals its negative.

The transpose of a matrix can be obtained by reflecting its elements across the main diagonal. Examples of transpositions can be seen here:

\$\begin{pmatrix}11&12&13\\21&22&23\end{pmatrix}\rightarrow\begin{pmatrix}11&21\\12&22\\13&23\end{pmatrix}\$

\$\begin{pmatrix}11&12&13\\21&22&23\\31&32&33\end{pmatrix}\rightarrow\begin{pmatrix}11&21&31\\12&22&32\\13&23&33\end{pmatrix}\$

The following matrix is antisymmetric, because it equals its transpose when multiplied by -1:

\$\begin{pmatrix}0&2&-1\\-2&0&0\\1&0&0\end{pmatrix}\$

All antisymmetric matrices exhibit certain characteristics. Antisymmetry can only be found on square matrices, because otherwise the matrix and its transpose would be of different dimensions. Additionally, elements which lie on the main diagonal must equal zero because they do not move and consequently must equal their negative, and zero is the only number which satisfies \$x=-x\$.

The Challenge

Given a square, non-empty matrix, check whether it is antisymmetric or not.

Rules

• This is code-golf so the shortest program in bytes wins.

• Input and output can assume whatever forms are most convenient.

• Assume only valid input will be given.

Test Cases

In: 1 1 1 1 1 1 1 1 1 Out: False In: 0 0 1 0 0 0 -1 0 0 Out: True In: 0 -2 2 0 Out: True ``` 

Antisymmetry of a Matrix code-golf matrix

A matrix is antisymmetric, or skew-symmetric, if its transpose equals its negative.

The transpose of a matrix can be obtained by reflecting its elements across the main diagonal. Examples of transpositions can be seen here:

\$\begin{pmatrix}11&12&13\\21&22&23\end{pmatrix}\rightarrow\begin{pmatrix}11&21\\12&22\\13&23\end{pmatrix}\$

\$\begin{pmatrix}11&12&13\\21&22&23\\31&32&33\end{pmatrix}\rightarrow\begin{pmatrix}11&21&31\\12&22&32\\13&23&33\end{pmatrix}\$

The following matrix is antisymmetric, because it equals its transpose when multiplied by -1:

\$\begin{pmatrix}0&2&-1\\-2&0&0\\1&0&0\end{pmatrix}\$

All antisymmetric matrices exhibit certain characteristics. Antisymmetry can only be found on square matrices, because otherwise the matrix and its transpose would be of different dimensions. Additionally, elements which lie on the main diagonal must equal zero because they do not move and consequently must equal their negative, and zero is the only number which satisfies \$x=-x\$.

The Challenge

Given a square, non-empty matrix, check whether it is antisymmetric or not.

Rules

• This is code-golf so the shortest program in bytes wins.

• Input and output can assume whatever forms are most convenient.

• Assume only valid input will be given.

Test Cases

In: 1 1 1 1 1 1 1 1 1 Out: False In: 0 0 1 0 0 0 -1 0 0 Out: True In: 0 -2 2 0 Out: True