What is matrices((X^tX)^{-1})^tX^ty ?

The solution to matrices((X^tX)^{-1})^tX^ty is emacitrsyX^{-t^2}

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simplify matrices((X^tX)^{-1})^tX^ty

simplify

ma t r i ces ((X^{t} X)^{- 1})^{t} X^{t} y

e ma c i t rsy X^{- t^{2}}

Solution steps

ma t r i ces ((X^{t} X)^{- 1})^{t} X^{t} y

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

X^{t} ((X X^{t})^{- 1})^{t} = (X (X X^{t})^{- 1})^{t}

= e ma c i t rsy (X (X X^{t})^{- 1})^{t}

Simplify

(X^{t} X)^{- 1} X : X^{- t}

= e ma c i t rsy (X^{- t})^{t}

(X^{- t})^{t} = X^{- t^{2}}

= e ma c i t rsy X^{- t^{2}}

(- 3 x y^{2} + 3 x^{2} y) (- 3 x y^{2} + 3 x^{2} y)

e^{- (3)}

2 x + 1^{2}

0.5 \cdot 0.5 \cdot (\frac{1.96}{0.05})^{2}

e^{- l n (c o s (t))}

What is matrices((X^tX)^{-1})^tX^ty ?
The solution to matrices((X^tX)^{-1})^tX^ty is emacitrsyX^{-t^2}