Manuals/calci/SKEWSYMMETRIC

SKEWSYMMETRIC(Order)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Order} is the order of the skew symmetric matrix.

Description

• This function shows the Skew Symmetric matrix with the given order.
• Skew Symmetric is also called Anti Symmetric or Antimetric.
• A Skew Symmetric is a square matrix which satisfies the following identity Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=A^T} ,where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^T} is the matrix transpose.
• If the entry in the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} row and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j^{th}} column is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ij}} .
• i.e.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = (a_{ij})} then the skew symmetric condition is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (a_{ij})} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -(a_{ij})} .
• So its diagonal values are "0".

Examples

1. SKEWSYMMETRIC(4)

0	-39	2	25
39	0	15	72
(-2)	-15	0	43
(-25)	-72	-43	0

2. SKEWSYMMETRIC(9)

0	48	-36	72	25	51	-13	-98	70
(-48)	0	-97	-33	78	-30	-56	62	45
36	97	0	42	-47	58	94	24	-43
(-72)	33	-42	0	-23	-77	-80	69	70
(-25)	-78	47	23	0	-17	17	-100	34
(-51)	30	-58	77	17	0	-43	-67	0
13	56	-94	80	-17	43	0	-24	55
98	-62	-24	-69	100	67	24	0	76
(-70)	-45	43	-70	-34	0	-55	-76	0

Related Videos

Skew Symmetric

See Also

• KURT
• STDEV
• STDEVP

References

• Skewness

• List of Main Z Functions

• Z3 home