blockmatrixformulas tex july 7 2015 block matrix formulas john a gubner department of electrical and computer engineering university of wisconsin madison abstract wederive a number of formulas for block matrices ...
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...Blockmatrixformulas tex july block matrix formulas john a gubner department of electrical and computer engineering university wisconsin madison abstract wederive number for matrices including the inverse determinant psuedoinverse etc if you nd this writeup useful or typos mistakes please let me knowatjohn wisc edu preliminary observations given b c d is invertible then schur complement bd it easy to check that i det detd we see only when taking yields instead assuming suppose comple mentofais ca detadet results using there are several identities can easily be found first comparing in particular n k cb bc inversion next upper left blocks which known as sherman morrison woodbury formula sometimes just remaining corresponding also equal example combining top row with bottom obtain anice application pseudoinverse recall m full rank its where complex conjugate transpose consider case h g by p andp itnoweasily follows positive semidenite amatrixu ispositive ifu u x ux all vectors use notatio...