When LabKitty t'was but a kitten, our favorite winter holiday tradition was the Twelve Days Of Christmas. Known to most as the song (and maybe one of those uncanny valley stop animations), the LK family spin on the classic took the form of gift giving, as things in the consumerism-crazed '80s often did.
In detail, mom would hang our Twelve Days of Christmas Gift-O-Rama on the wall, a discarded turnout blanket onto which she (actually, my crazy aunt now that I think of it) had sewn a staggered row of twelve festive numbered pockets and into each of which was tucked a wrapped present. These were opened one per morning, in order, starting on December 12 (because 12 + 12 = 25. Dur-hey).
The gifts were simple gewgaws or candy, for it was an innocent time, years before the throes of adolescence would demand more demanding fare such as xboxes and carcanos (which did not fit into the wee pockets). But me and my sister loved the heck out of the TDoC while it lasted, if for no other reason than trying to guess tomorrow's gift via surreptitious wrapping paper squeezings when mom was out of earshot.
It's the sort of folksy tale Sarah Vowell or David Sedaris might relate on NPR. However, we here at the LabKitty are academics and academics are contractually obligated to crush the fun out of childhood memories, be they jump rope atrocities, baby doll penises, or, in this case, sing-song affirmation of the corrupt marriage between late-stage capitalism and a cherry-picked Judeo-Christian value system.
In that spirit, I give you The Twelve Days of Eigenvalues.
World Eigenvalue Day is February 14th. It's a proclamation that will get you dumb looks almost everywhere, but faithful LabKitty readers circle the date and prepare the festivities far in advance. This year, beyond the traditional drinking, gift giving (see below), Sex Bomb dance (the Tom Jones version, not the Flipper one), and drinking, we add the x Days of Eigenvalues, where x is a number between one and however many interesting eigenvalue factoids I can dig up. One per day, starting on day 14-x. If you are reading this then apparently 14-x is today's date.
From here out, one factoid will appear each morning until the day of days, or will assuming I can work the Blogger autopost feature, which is always a coin flip. Enjoy.
Note added in proof: I really did consider posting these one at a time on x days leading up to Eigenvalue Day as stated, but in the end did the kibosh on the idea concerned the result not nearly as cool as it was in my head, which one day will be the title of my autobiography. Also, doing so would require I can work the Blogger autopost feature, which is always a coin flip. I may have mentioned that already.
Long story short: you get them all at once. Today. Here they are. Enjoy.
In detail, mom would hang our Twelve Days of Christmas Gift-O-Rama on the wall, a discarded turnout blanket onto which she (actually, my crazy aunt now that I think of it) had sewn a staggered row of twelve festive numbered pockets and into each of which was tucked a wrapped present. These were opened one per morning, in order, starting on December 12 (because 12 + 12 = 25. Dur-hey).
The gifts were simple gewgaws or candy, for it was an innocent time, years before the throes of adolescence would demand more demanding fare such as xboxes and carcanos (which did not fit into the wee pockets). But me and my sister loved the heck out of the TDoC while it lasted, if for no other reason than trying to guess tomorrow's gift via surreptitious wrapping paper squeezings when mom was out of earshot.
It's the sort of folksy tale Sarah Vowell or David Sedaris might relate on NPR. However, we here at the LabKitty are academics and academics are contractually obligated to crush the fun out of childhood memories, be they jump rope atrocities, baby doll penises, or, in this case, sing-song affirmation of the corrupt marriage between late-stage capitalism and a cherry-picked Judeo-Christian value system.
In that spirit, I give you The Twelve Days of Eigenvalues.
World Eigenvalue Day is February 14th. It's a proclamation that will get you dumb looks almost everywhere, but faithful LabKitty readers circle the date and prepare the festivities far in advance. This year, beyond the traditional drinking, gift giving (see below), Sex Bomb dance (the Tom Jones version, not the Flipper one), and drinking, we add the x Days of Eigenvalues, where x is a number between one and however many interesting eigenvalue factoids I can dig up. One per day, starting on day 14-x. If you are reading this then apparently 14-x is today's date.
From here out, one factoid will appear each morning until the day of days, or will assuming I can work the Blogger autopost feature, which is always a coin flip. Enjoy.
Note added in proof: I really did consider posting these one at a time on x days leading up to Eigenvalue Day as stated, but in the end did the kibosh on the idea concerned the result not nearly as cool as it was in my head, which one day will be the title of my autobiography. Also, doing so would require I can work the Blogger autopost feature, which is always a coin flip. I may have mentioned that already.
Long story short: you get them all at once. Today. Here they are. Enjoy.
The Twelve Days of Eigenvalues
- If λ is an eigenvalue of A, then λ ≤ | A |, where | A | is any matrix norm.
- If xtA x ≥ 0 for every vector x, then all the eigenvalues of A are positive.
- The determinant of A is equal to the product of the eigenvalues of A.
- The eigenvalues of a block matrix are the eigenvalues of the blocks.
- If λ is an eigenvalue of A, then λ2 is an eigenvalue of A 2.
- If λ is an eigenvalue of A, then λ-1 is an eigenvalue of A-1.
- The eigenvalues of A are the same as the eigenvalues of A t.
- The trace of A is equal to the sum of the eigenvalues of A.
- The eigenvalues of a symmetric matrix are real.
- Something something nilpotent.
- eig(A+cI) = eig(A) + c.
- eig(AB) = eig(BA).
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