Q:

How does this code work?

I found this piece of C++ code on a forum that I can't fully understand. Since I don't have their library that performs matrix/vector math, I need to manually figure it out and replicate the functionality.
Calculate Euler rotation angles between 2 vectors .. we use Rodrigues formula
    vector $V1 = << my first vector >>;
    vector $V2 = << my second vector >>;

    vector $axis;
    float $angle;

    $angle = acos($V1*$V2);
    $axis = normalizeVector((cross($V1,$V2)));

    matrix $axis_skewed[3][3] = <<
    0, (-$axis.z), ($axis.y) ;
    ($axis.z), 0, (-$axis.x) ;
    (-$axis.y), ($axis.x), 0 >>;

    matrix $eye3[3][3] = <<
    1, 0, 0;
    0, 1, 0;
    0, 0, 1 >>;

From here onwards things get tricky:
    // here's Rodrigues
    $R = $eye3 + sin($angle)*$axis_skewed + (1-cos($angle))*$axis_skewed*$axis_skewed;

do you add all the properties of the eye3 matrix?
do you multiply with all the properties of the axis_skewed matrix?
and what is R? a vector or matrix? or number?
This is simple.
    matrix $vectorMatr[3][1];
    $vectorMatr[0][0] = ($V1.x);
    $vectorMatr[1][0] = ($V1.y);
    $vectorMatr[2][0] = ($V1.z);

Again, this is tricky:
    // $result is the resulting vector

    $result = ($R * $vectorMatr);

do you multiply the vector with the matrix to get the resultant vector using standard matrix multiplying?
do you multiply the two matrix's and then transform the point using the matrix?

A:

I'm pretty sure that's psuedocode.  It's definitely not C++.  All the functions are pretty self explanatory.
acos() --- self explanatory
$V1 * $V2 --- dot product
(note:, that would normally be interpreted as a regular matrix multiplication, but but in the context of "float $angle = acos($V1*$V2);", it doesn't make sense as anything other than a dot product)
cross() --- cross product
normalizeVector() --- self explanatory
sin($angle)*$axis_skewed --- this is a scalar multiply
get it?
EDIT
$R = $eye3 + sin($angle)*$axis_skewed + (1-cos($angle))*$axis_skewed*$axis_skewed;
$eye3 -- is a 3x3 matrix
sin($angle)*$axis_skewed --- this is a scalar multiply, resulting in another 3x3 matrix
(1-cos($angle))*$axis_skewed --- this is a scalar multiply, resulting in another 3x3 matrix
(previous)*$axis_skewed --- this is a regular matrix multiplication, resulting in another 3x3 matrix
That leaves us with:
$R = [3x3 matrix] + [3x3 matrix] + [3x3 matrix]
Which is just regular entrywise matrix addition.

