Showing That a Function Is an Inner Product In
Chapter 5, Problem 27(choose chapter or problem)
Showing That a Function Is an Inner Product In Exercises 27 and 28, let
\(A=\left[\begin{array}{ll} a_{11} a_{12} \\ a_{21} a_{22} \end{array}\right]\) and
\(B=\left[\begin{array}{ll} b_{11} b_{12} \\ b_{21} b_{22} \end{array}\right]\)
be matrices in the vector space \(M_{2,2}\). Show that the function defines an inner product on \(M_{2,2}\).
\(\langle A, B\rangle=a_{11} b_{11}+a_{12} b_{12}+a_{21} b_{21}+a_{22} b_{22}\)
Text Transcription:
A = [a_11 a_12 \\ a_21 a_22]
B = [b_11 b_12 \\ b_21 b_22]
M_{2, 2}
langle A, B rangle = a_11 b_11 + a_12 b_12 + a_21 b_21 + a_22 b_22
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