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 4h comment Prove positive definite of a function @LuhShyyeuan if you are going to reorganize the problem, then create a new post for that question. 4h comment Measurability properties of functions Hint: $g(x) = x^n$ is a continuous function 4h comment Prove positive definite of a function @LuhShyyeuan perhaps it would help if you explained why you expect this to be true in a certain context. 4h comment Prove positive definite of a function @LuhShyyeuan that also won't help. Take $X = 1000I$, $A = (1/100)I$ and $Q = 2I$. 4h comment If every borel measurable function continuous in compact metric space then metric space is finite @GEdgar apparently yes. 4h comment prove that √2 * π is irrational primes devided 4 is 3 These are 2 different tasks, so you should ask about them in two separate questions. Also, you should provide context for your questions. What is the level of your mathematical background, for example? Are these questions from class? From a book? 4h comment A purely algebraic proof of $\vec{a}\cdot \vec{b} = \lVert\vec{a} \rVert\lVert\vec{b} \rVert\cos(\theta)$ @JohnDoe $\arccos(x)$ only makes sense if $|x| \leq 1$. How do you know that $$|x| = \frac{|\vec u \cdot \vec v|}{\|\vec u\| \|\vec v\|} \leq 1?$$ 4h comment Prove positive definite of a function @LuhShyyeuan it won't change anything. Take instead $$A = (1/100)I$$ and the same thing happens (for a different $n$, possibly). 4h comment Compute the Jordan form of a particular matrix @Travis good catch, and thanks. 4h comment A purely algebraic proof of $\vec{a}\cdot \vec{b} = \lVert\vec{a} \rVert\lVert\vec{b} \rVert\cos(\theta)$ @JohnDoe fixed the comment. 4h comment A purely algebraic proof of $\vec{a}\cdot \vec{b} = \lVert\vec{a} \rVert\lVert\vec{b} \rVert\cos(\theta)$ @JohnDoe to clarify your edit: it seems that you define the angle between two unit vectors to be given by $$\theta = \arccos(\vec u \cdot \vec v)$$ Note that in order for this definition to make sense, you'll need the Cauchy-Schwarz inequality. 4h revised Compute the Jordan form of a particular matrix added 53 characters in body 4h answered Compute the Jordan form of a particular matrix 5h revised Prove that $ABA^T$ is symmetric when $A$ and $B$ are symmetric matrices edited tags 5h answered Prove that $ABA^T$ is symmetric when $A$ and $B$ are symmetric matrices 7h answered Prove positive definite of a function 8h comment isomorphism from one vector space to another one Did you try looking in the index of your textbook? 1d comment If $AB = BA$ and $AC = CA$, prove that $BC = CB$ Hint Show that if $A$ is diagonal, then $B$ and $C$ are both diagonal. 1d comment Finding the Generalized Eigenspace @AriNubar as Peter said, there must be a mistake in the question itself or in the way that you copied it. 1d awarded continuity