ColumnSpaceProjection
Finds the projection of a vector onto the column space of a matrix.
Syntax
-
ColumnSpaceProjection(A, v)-
Ais a matrix -
vis a vector
-
Description
If A is a matrix of size n×m and v a vector of dimension n, then ColumnSpaceProjection(A, v) is the projection of v onto the column space of A.
Examples
A ≔ ❨❨2, 2, −5, 0, −1❩, ❨1, 5, −2, 1, 5❩, ❨0, 1, 3, 2, 6❩, ❨−2, 1, 4, 6, 9❩, ❨3, −2, 7, −2, 6❩❩
⎛ 2 2 −5 0 −1⎞ ⎜ 1 5 −2 1 5⎟ ⎜ 0 1 3 2 6⎟ ⎜−2 1 4 6 9⎟ ⎝ 3 −2 7 −2 6⎠
ColumnSpaceProjection(A, ❨1, 2, 1, 0, 1❩)
⎛0.971874108932⎞ ⎜2.07377282903 ⎟ e⎜0.710902726238⎟ ⎜0.10558736155 ⎟ ⎝ 1.0645512254 ⎠