Linear Algebra and the C Language/a0ll

__NOTOC__ Projection onto a vector subspace: Use these two algorithms to calculate the projection of x onto R3. * A is a subspace of R3. Find the matrix V that projects a vector x onto R3. Proj(x) = [A inv(AT A) AT] x = V x * B is a basis for the orthogonal complement of AT. Find the matrix V that projects a vector x onto R3. Proj(x) = [Id - B inv(BT B) BT)] x = V x ... Wikipedia: Projection (linear algebra) Examples of applications in R3 Find the transformation matrix for a projection onto R3: Proj(x) = [A inv(AT A) AT] x c03a.c Verify if AT is a basis for a Row Space by Row Reduction: c03b.c Find a basis B for the orthogonal complement of AT. c03c.c Find the transformation matrix for a projection onto R3: Proj(x) = [Id - (B inv(BT B) BT)] x c03d.c Examples of applications in R4 Find the transformation matrix for a projection onto R4: Proj(x) = [A inv(AT A) AT] x c04a.c Verify if AT is a basis for a Row Space by Row Reduction: c04b.c Find a basis B for the orthogonal complement of AT. c04c.c Find the transformation matrix for a projection onto R4: Proj(x) = [Id - (B inv(BT B) BT)] x c04d.c Examples of applications in R5 Find the transformation matrix for a projection onto R5: Proj(x) = [A inv(AT A) AT] x c05a.c Verify if AT is a basis for a Row Space by Row Reduction: c05b.c Find a basis B for the orthogonal complement of AT. c05c.c Find the transformation matrix for a projection onto R5: Proj(x) = [Id - (B inv(BT B) BT)] x c05d.c