First all of all, I am sorry I have put a page of my text book. Somehow I need some help to understand some paragraphs in the page. If you can explain, please let me have some explanations to those in the image.
Thank you in advance.
2026-03-27 23:31:20.1774654280
Some detail needed in Positive Definite Matrix
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Not sure what there is to explain about 1 and 3. I will say that the second equation follows by block-matrix multiplication: $$ \pmatrix{e_1'\\e_2'} \pmatrix{x_1\\x_2} = \pmatrix{e_1'\\e_2'} (x) = \pmatrix{e_1'x\\e_2'x}= \pmatrix{y_1\\y_2} $$