I've been beating my head against this problem for hours. I see numerically that two expressions are equal, but I can't prove it:(adsbygoogle = window.adsbygoogle || []).push({});

(J[itex]^{T}[/itex]R[itex]^{-1}[/itex]J + P[itex]^{-1}[/itex])[itex]^{-1}[/itex]J[itex]^{T}[/itex]R[itex]^{-1}[/itex]

=

PJ[itex]^{T}[/itex](JPJ[itex]^{T}[/itex] + R)[itex]^{-1}[/itex]

J is arbitrary size, P and R are square though not necessarily equal. Can anyone help? I thought binomial inverse theorem would save me but I haven't been able to get rid of the extraneous terms.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help proving equality of matrix expressions

**Physics Forums | Science Articles, Homework Help, Discussion**