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Introduction to Linear Algebra

Exercise 2.7.19

Answers

(a): The transpose of $A^{T} SA$ is $A^{T} S^{T} A^{T} T = A^{T} SA = n$ by $n$ when $S^{T} = S$ (any $m$ by $n$ matrix $A$ ).
(b): ${(A^{T} A)}_{jj} = (column j$ of $A) \cdot (column j$ of $A) = ($ length squared of column $j) \geq 0$ .

mathchakra

2022-01-16 12:27

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