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isOrthogonal -- whether a matrix is orthogonal

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 = | -13642637776303/25784639135203 12229430856720/25784639135203 
     | -10626966502320/25784639135203 -22299982236003/25784639135203
     | -8578873737630/25784639135203  898411676400/25784639135203   
     | 526353961350/25784639135203    -2074373150080/25784639135203 
     | -17085652158960/25784639135203 3590161698480/25784639135203  
     ------------------------------------------------------------------------
     -488309514210/1983433779631  12456308748450/25784639135203 
     -101074680000/1983433779631  3866314812080/25784639135203  
     -1465692522094/1983433779631 -13169245762575/25784639135203
     -390527545275/1983433779631  17151229337322/25784639135203 
     1176682179960/1983433779631  -5210172332400/25784639135203 
     ------------------------------------------------------------------------
     11563305687360/25784639135203  |
     6160444867920/25784639135203   |
     -7345702213920/25784639135203  |
     -18447991409400/25784639135203 |
     -9944785964803/25784639135203  |

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

o4 = true

See also

Ways to use isOrthogonal:

  • isOrthogonal(Matrix)

For the programmer

The object isOrthogonal is a method function with options.


The source of this document is in DeterminantalRepresentations.m2:925:0.