Vector Operations
| v[[i]] or Part[v,i] | give the i element in the vector v |
| c v | scalar multiplication of c times the vector v |
| u.v | dot product of two vectors |
| Norm[v] | give the norm of v |
| Normalize[v] | give a unit vector in the direction of v |
| Standardize[v] | shift v to have zero mean and unit sample variance |
| Standardize[v,f1] | shift v by  and scale to have unit sample variance |
Basic vector operations.
This is a vector in three dimensions.
| Out[1]= |  |
This gives a vector
in the direction opposite to
with twice the magnitude.
| Out[2]= |  |
This reassigns the first component of
to be its negative.
| Out[3]= |  |
This gives the dot product of
and
.
| Out[4]= |  |
This is the norm of
.
| Out[5]= |  |
This is the unit vector in the same direction as
.
| Out[6]= |  |
This verifies that the norm is 1.
| Out[7]= |  |
Transform
to have zero mean and unit sample variance.
| Out[8]= |  |
This shows the transformed values have mean 0 and variance 1.
| Out[9]= |  |
Two vectors are orthogonal if their dot product is zero. A set of vectors is orthonormal if they are all unit vectors and are pairwise orthogonal.
| Projection[u,v] | give the orthogonal projection of u onto v |
| Orthogonalize[{v1,v2,...}] | generate an orthonormal set from the given list of vectors |
Orthogonal vector operations.
This gives the projection of
onto
.
| Out[10]= |  |
is a scalar multiple of
.
| Out[11]= |  |
is orthogonal to
.
| Out[12]= |  |
Starting from the set of vectors
, this finds an orthonormal set of two vectors.
| Out[13]= |  |
When one of the vectors is linearly dependent on the vectors preceding it, the corresponding position in the result will be a zero vector.
| Out[14]= |  |
