Are all eigenvalues of $X^TX$ pairwise disjunct if $X$ is both normal and symmetric?

Let $X in mathbb{R}^{n,n}$ be a normal matrix. I am supposed to show that if all eigenvalues of $X^TX$ are pairwise disjunct, then $X$ is symmetric.

Does anyone have any tipps on how to do this?

relational database – Is there a normal form for exactly identical tables?

Consider this design in a relational database:

There are two tables A, B, both having two columns X, Y. The constraints are:

  1. X in both tables are the primary keys. (The values are unique in each table.)
  2. The data in both tables must be exactly identical. (Each insert, delete, update request must be applied to the two tables together.)

It is obviously not an ideal design. But does it not conform to some normal forms? Which normal form and why?

Does the same hold if there is another column in both tables but not identical? Or some rows are removed in one table?

How do I get a normal disk going (PERC H710 Mini) with perccli?

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I have a Dell PowerEdge R720 which boots up and has 1.7 TB of drive space but I can’t seem to get any of it and use it. When I try and install Fedora there are no available drives to install it to.

I need to use perccli to run a command to make either all or some of this 1.7 TB available as a drive right?

I ran "perccli64 /c0 add vd each r0 drives=32:1-7"

Thinking this would give me some new drives when I run "df" but it did not.

The images above show output of current setup.

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pathfinder 1e – Can a spellcaster use spell slots above their normal limit if their ability scores allow bonus spells of that level?

This question is inspired by discussion here, about how Heighten Spell works with Reserve Feats. The question that I am asking here deals with whether or not players can cast spells using spell slots for spell levels that they don’t have access to yet.

I feel like an example would explain this concept best.

Take Xylitol, the first-level wizard with an intelligence of 18. He has 5 0th-level spells per day and 3 1st level spells per day from his class. He also has 1 bonus 1st level spell per day from his high intelligence. The Ability Modifiers and Bonus Spells table says that he also has 1 bonus spell of each 2nd, 3rd, and 4th levels.

The question is this: Can Xylitol cast 1st level spells using the bonus slots for his 2nd, 3rd, and 4th level spells? He clearly can’t cast spells that are inherently higher level than 1st, since he can’t learn them, but can he cast 1st level spells using bonus 2nd, 3rd, and 4th level slots?

This has come up on these boards before, here. What I’m looking for here is a clear rules citation that clarifies this one way or the other. The wording in the section on ability scores makes it quite clear that characters cannot cast spells that are actually higher level than their class allows them to cast, but it is not clear that these higher level slots are barred until the appropriate spell level is unlocked. If a character has access to a spell level that they can’t use because their ability score isn’t high enough, they can freely use those slots for lower level spells, so why can’t they use their bonus spell slots for lower level spells?

As KRyan’s answer says, the Basics section covers this. Based on questions and comments both here and elsewhere, that section seems to be worded ambiguously enough that it’s caused confusion. I’d like to find another, more clear wording to this rule if at all possible.

Answers from either D&D 3.5 or Pathfinder are acceptable, but please note which one your answer applies to.

N.B. I’d like to note that I personally don’t feel that players should have access to higher level slots like this. There are a large number of locations where it’s heavily implied that this is not the case, but I feel that finding a clear rules citation here would be helpful. I can’t find one that is clear for either interpretation here.

network – NMAP Scan Shows Ports for VNC, RDP, SAMBA & SSH on iOS – is this normal?

I ran an nmap scan on my iPad’s IP address and the results showed the following ports listed below available in a filtered state. See screenshot for the actual terminal results. This can’t be normal, right? There are no apps installed that would explain these ports and the device is not jailbroken.

nmap results
ms-wbt-server (Remote Desktop)
4 different VNC ports
And an iPhone Sync port

Context free grammar to chomsky normal form bruh

I’ve had this question bugging me for so long but i cant seem to solve the question can anyone help?

S 🡪 [ R ]

R 🡪 [ Q ] | T

T 🡪 j R | ε

Q 🡪 i k | ε

automata – Context Free Grammar to Chomsky Normal Form Help

I am trying to convert the following CFG to CNF:

S -> ABS | ε
A -> BSBa | a
B -> Ba | a

The finally result looks like this:

S -> AS’ | AB
S’ -> BS
A -> S’B’ |BB’ | X
B’ -> BX
X -> a
Y -> b
B -> BX | XY

I am fairly new to chomsky normal form, so can anyone verify that I did this right?
Thank you in advance!

performance – iMac that slow – is that normal?

I have a iMac Retina4K from the end of 2015 with 3.1GHz Quad-Core i5 and 8GB DDR3. My OS is catalina and I am using Firefox, Adobe InDesign and Adobe Illustrator most of the time. Since I upgraded to Catalina my Mac is soooo slow that starting the mac at morning until anything really runs (I am able to click on an app) takes up to 10 minutes (no application opened yet).

Opening up Illustrator works in 6 of 10 times, else it just freezes. If opened it does work okay though. Firefox freezes also on a regular basis. I never open up more then 3 applications at the same time, have no widget etc running and I got hundreds of gigabyte diskspace left.

I get it, that this isn’t the newest device but shouldn’t the OS and some really simple task like opening up a browser be “there” in less then 5 minutes?

My question though is a different one: If I’d set up/reinstall the Mac completely new with Catalina (as I am bound by Creative Cloud to it) should that speed up my described routine or is the current scenario just what I can expect from the combination of that hardware/software combination?

Is it normal for my CPU to appear locked at 4.68 GHz when its base speed shows 3.6 GHz?

No games or anything significant is running on my PC. I noticed this and it just seems really weird, it seems to be locked a 4.68GHz:

enter image description here

I’m wondering if maybe I overclocked it and forgot. I’m pretty naïve as far as far as hardware goes. Does this really mean its running at 4.68GHz constantly, or am I misunderstanding the UI?