Showing That a Function Is an Inner Product In Exercises 27 and 28, letA =

Chapter 5, Problem 28

(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 \(M_{2,2}\).

\(\langle A, B\rangle=2 a_{11} b_{11}+a_{12} b_{12}+a_{21} b_{21}+2 a_{22} b_{22}\)

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 = 2a_11 b_11 + a_12 b_12 + a_21 b_21 + 2a_22 b_22