# Scalars Assignment | Assignment Help Services

A matrix A E NA ( HR ) is said to be positive definite if U’ AU &gt; O for cachnon – 2010 Vector UE THEM.( 1) Show that the set of positive – definite matrices is closed under addition , and underscalar multiplication by positive scalars .

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The geometric picture here is that the set.of positive – definite matrices , while not a subspace , is a &quot; conc ! )( ii ) Show that a diagonal matrix A is positive definite if and only if all of its diagonalentries are positive .( jjj ) Given a symmetric , positive definite matrix A , show that ( V , W ) A : = UT Aw definesall inner product on Them.&quot;( iv ) Show that , conversely , every inner product on {~ is of the above form , for somesymmetric , positive definite matrix A.

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