Orthogonal Projections- not invertible A * A

504 Views Asked by At

One of my homework problems asks to find the matrices of orthogonal projections onto all four fundamental subspaces.

For the projection onto the range of the matrix, I used

projection of Range of A = A((A * A)inverse)A *.

But the A * A is not invertible, so I was wondering where to go from here? Is there a different equation I can use in this situation?

If anyone is curious, the matrix is

1 1 1

1 3 2

2 4 3

*I have figured out what my issue was, I needed an orthogonal basis. Now I have figured out the protection for Ran (A *) and Ran (A). By definition, Ran A = Ker( A *) Transpose, so does that mean Ran A transpose = Ker ( A *)?