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isOrthogonal -- whether a matrix is orthogonal

Synopsis

Description

This method determines whether a given matrix is orthogonal, i.e., has inverse equal to its transpose.

When working over an InexactFieldFamily like RR or CC, the option Tolerance can be used to specify the internal threshold for checking equality (any floating point number below the tolerance is treated as numerically zero). If the given matrix does not have floating point entries, then this option is not used.

i1 : O1 = randomOrthogonal 5

o1 = | .442386  -.0306554 .751799   -.317548 .370563  |
     | .133864  .768167   -.0944111 -.513838 -.345046 |
     | -.60855  -.385718  .234815   -.587034 -.284854 |
     | -.42001  .39448    .591227   .519553  -.220209 |
     | -.489525 .323399   -.145593  -.143489 .783576  |

                5         5
o1 : Matrix RR    <-- RR
              53        53
 
i2 : isOrthogonal O1

o2 = true
 
i3 : O2 = randomOrthogonal(5, QQ)

o3 = | -22142569999/27593776175 90555408/788393605   -5532008344/27593776175
     | 193172688/788393605      145827307/157678721  24042978/788393605     
     | 591854008/5518755235     -5780466/157678721   -5151709442/5518755235 
     | -598559432/27593776175   -200993706/788393605 7495643483/27593776175 
     | -84039992/157678721      40244400/157678721   18443792/157678721     
     ------------------------------------------------------------------------
     -5025793592/27593776175  2046480376/3941968025 |
     -216954846/788393605     70436016/788393605    |
     -1194249041/5518755235   -206975072/788393605  |
     -25053509506/27593776175 -751964432/3941968025 |
     22251808/157678721       -123874657/157678721  |

              5       5
o3 : Matrix QQ  <-- QQ
 
i4 : isOrthogonal O2

o4 = true

See also

Ways to use isOrthogonal :

For the programmer

The object isOrthogonal is a method function with options.