Talk:Moore–Penrose inverse/to do

Verify
 * Verify that conjugate transposition must be used in the second limit expression.
 * Verify whether the prose regarding the projections onto kernel and range is valid.
 * Verify the Penrose 1956 reference (doing this... --RainerBlome 22:31, 17 September 2007 (UTC)).

Cleanup Expand
 * Explain notations in the beginning of the article. ✅
 * Show that $$A^+x$$ is the minimum-norm, least-squares solution to any SLE (yes, it is, not just overdetermined ones). Add a case-by-case analysis for the cases where b is in range(A) and where it is not.
 * Add geometric definition or geometric explanation of what the pseudoinverse does. ✅
 * Add Moore's definition of the pseudoinverse.
 * Show that all three definitions are equivalent.
 * Add Examples section. ✅
 * Add application example: linear regression.
 * Explain the role of projections for the Pseudoinverse ($$AA^*$$, $$A^*A$$; Done: $$AA^+$$ and $$A^+A$$).
 * Check in how far it makes sense to view any of the above projections as a correlation matrix.
 * Add projection properties. ✅
 * Determine under which conditions $$(A^*A)^{-1}$$ or $$(AA^*)^{-1}$$ exist. Is the existence equivalent to "A is overdetermined with independent columns"?
 * As far as possible, get rid of the dependency on $$(AA^*)^{-1}$$ (in the current In the application section).
 * Add history section (move part of the intro there)
 * Show computation using SVD. ✅
 * Show incremental computation.
 * Show numerical complexity of computations.
 * Translate section about generalized inverses from German Pseudoinverse page.