cspice_invort

 Abstract I/O Examples Particulars Required Reading Version Index_Entries

#### Abstract

```
CSPICE_INVORT returns the inverse of a 3x3 matrix with orthogonal
columns and non-zero norms using a numerical stable algorithm.

```

#### I/O

```
Given:

m     a 3x3 matrix.

[3,3] = size(m); double = class(m)

the call:

mit = cspice_invort(m)

returns:

mit   the matrix obtained by transposing 'm' and dividing the rows by
squares of their norms.

[3,3] = size(mit); double = class(mit)

```

#### Examples

```
Suppose that you have a matrix 'm' whose columns are orthogonal
and have non-zero norm (but not necessarily norm 1).  Then the
routine cspice_invort can be used to construct the inverse of 'm':

invers = cspice_invort( m )

```

#### Particulars

```
Suppose that m is the matrix

-                      -
|   A*u    B*v     C*w   |
|      1      1       1  |
|                        |
|   A*u    B*v     C*w   |
|      2      2       2  |
|                        |
|   A*u    B*v     C*w   |
|      3      3       3  |
-                      -

where the vectors (u , u , u ),  (v , v , v ),  and (w , w , w )
1   2   3      1   2   3          1   2   3

are unit vectors. This routine produces the matrix:

-                      -
|   a*u    a*u     a*u   |
|      1      2       3  |
|                        |
|   b*v    b*v     b*v   |
|      1      2       3  |
|                        |
|   c*w    c*w     c*w   |
|      1      2       3  |
-                      -

where a = 1/A, b = 1/B, and c = 1/C.

```

#### Required Reading

```
For important details concerning this module's function, please refer to
the CSPICE routine invort_c.

MICE.REQ

```

#### Version

```
-Mice Version 1.0.0, 14-NOV-2013, EDW (JPL), SCK (JPL)

```

#### Index_Entries

```
Transpose a matrix and invert the lengths of the rows
Invert a pseudo orthogonal matrix

```
`Wed Apr  5 18:00:33 2017`