 healing mist on his skin. And the ice blades he controlled just now. He had transcended the limits of his body and naturally knew how to control the power between the sky and the ground. He had temporarily reached hero rank. He was at the fourth rank now!Q: Conditions for a Function $T\colon\mathbb{R}^{n\times n}\rightarrow \mathbb{R}^{n\times n}$ to Drop Rank Let $T\colon\mathbb{R}^{n\times n}\rightarrow \mathbb{R}^{n\times n}$ and suppose that $\text{rank} \ T(I_n) = n$. Under what conditions is it true that there exists a neighborhood $N_I$ of the identity such that, for all $A\in N_I$, $\text{rank} \ T(A) = n$?
Can stronger conditions be provided in the case where the range of the function is a subset of the positive semidefinite matrices of dimension $n$?

A: $T$ being continuous at $I_n$ is sufficient.
All $(n-1)\times(n-1)$ minors of $T(I_n)$ are non-zero, minors are continuous functions, and there are only finitely many of them, meaning there is some $\varepsilon>0$ such that we have an open ball of radius $\varepsilon$ around $T(I_n)$ with only invertible matrices. By continuity of $T$, there is a $\delta>0$ such that setting $N_I$ to be the open $\delta$-ball around $I$ works.
The new lithographic printing techniques from Germany produced the first hand-colored campaign prints for the 1844 election. The demand for political prints grew and the 1880s color printing innovations produced a revolution that saw dozens of well-designed posters for the campaigns of William McKinley and William Jennings Bryan in 1896 and 1900. After 1912 a few colorful posters were appeared in each campaign, mostly printed by the new offset process, but it was the rise of Democratic insurgents in the 1960s that brought about the next great explosion of political posters. The 1968 candidacy Eugene McCarthy motivated artists to produce posters beyond offset—screen print, spray paint stencil, collage assemblage, and occasionally hand drawn. In 1972, the George McGovern campaign was alive with hundreds of creative posters and prints. In 2008 the candidacy of Barack Obama inspired artists to produce another marvelous outburst of posters using a wide variety of printing techniques. The historical development of the campaign poster, its relationship to technology and its effectiveness in using visual language to persuade voters is the central focus of this article that includes thirty-one outstanding examples in full color online.The Chameleon Cafe in Maple Ridge, British Columbia is a casual dining restaurant that offers an innovative menu that has gained quite a following. We are currently seeking an dynamic Host/Hostess to join our team and be the first point of contact for our guests, an invaluable asset to our staff, who loves their job as much as we do.
• Good verbal and written communication (English).
• Availability to work varied shifts including days, evenings and weekends as required.
• Wage: $13-15 hourly based on experience and qualifications.For my fellow book lovers, I just wanted to briefly talk about a few of my favorite books and series.
- Harry Potter series – I’m always amazed by the way J.K. Rowling creates an entire (and very complex) world within these seven books. Over the years I’ve read and re-read them several times. These books are what I turn to when I don’t know what to read or want to cure my boredom.
- A Series of Unfortunate Events series – Lemony Snicket is extremely clever. I loved that as a kid, and I love it now. Although these books (like the Harry Potter series and a couple other books on this list) are meant for children, they’re still wildly entertaining and so strange that you just have to keep reading.
- Miss Peregrine’s Home for Peculiar Children series – These books by Ransom Riggs are newer than the other two series I mentioned, and they’re by far the most odd, which says a lot. Based on creepy old photographs that are included in the books, these novels have romance, comedy, action, and some really good dialogue as well.
- Someone Like You by Sarah Dessen – When I first read this, I was too young to fully understand what it was talking about (it’s about boys, and loss). But as I re-read it, it never fails to strike a chord with me. I think all girls go through something like Halley (the protagonist) does while in high school.
- The Book Thief by Markus Zusak – This book has one of the most fascinating concepts I’ve ever read. Told from the perspective of Death and centering on one girl and her life, the novel never fails to completely captivate the reader.
- Room by Emma Donoghue – If you saw the movie and liked it, read the book immediately. Told from the perspective of a five-year-old, this novel shows how deep the bond between mother and child is, while also displaying the pure innocence of children even when in the presence of evil.
- The Girl with the Dragon Tattoo by Stieg Larsson – Even though it has about five storylines going on, this novel is incredible. The characters are extremely well-developed, and the plot is shocking. This is a great read for anyone who loves thrillers that start out slow.
- Thirteen Reasons Why by Jay Asher – As someone who has struggled quite a bit with depression, this book holds a special place in my heart. It’s basically the story of a girl who committed suicide and left a suicide note on a cassette tape explaining why she did it. It shows why the little things matter, and hopefully inspires others to think about the way people may be feeling even if they don’t show it on the outside.
- The Host by Stephenie Meyer – Okay, I was not a big fan of the Twilight books, but this one was something much different. The Host is so much more complex and well thought-out than Stephenie Meyer’s other books. Relationships between characters are well-developed, and the storyline is intriguing enough to keep you reading for several hundred pages.
- The City of Ember series by Jeanine DuPrau – Yes, this is another series written for children, but it’s a post-apocalyptic series and that’s something I just can’t resist. I love reading about the worlds authors create after the world we know has been destroyed. I love contemplating how different life could be if we lived the way the people in the city of Ember do, for example.
- Flowers in the Attic series by Virginia Andrews – These books may take some time to get into, but once they grab your attention, you’re hooked. I can’t explain how fascinating the story of these four children (adults, eventually) is or how complex the relationships between siblings become.
What’s your all-time favorite book? Give me some recommendations in the comments below!
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Harry Potter, The flowers in the attic and the book thief are so amazing! I was so surprised to see the Book thief on your list! I’ve never known of anyone else to read it! I’m definitely going to Check out the other books on this list! Thanks for sharing 😊
LikeLiked by 1 personDan Schawbel came up with a great idea to start a Personal Branding Wiki. Given the explosion of the personal branding craze, a wiki is a phenomenal idea. In short, the definition and ideas about personal branding continue to evolve as more ideas pour in–what better way to organize those thoughts than to have a wiki?
More important than the actual wiki, I must say that I am quite impressed with Dan Schawbel. Interest in Personal Branding is rising–why not be the defacto thought leader by being the first to market with a personal branding magazine, wiki, videos, etc.
There is something we can all learn from Dan Schawbel. Do you have an idea? Are you creating a following with that idea? Then make sure to keep innovating. That is the one thing Dan Schawbel is doing absolutely right.
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Thanks for this…I think it’s a valuable excercise!Just to point out there is a lot of editing in some of these pictures of the buildings with the eclipse. I had a lot of photos with very white backgrounds and decided to play around a bit.
Hello again pretty people!I'm still here and still going with posting, only like 3 months until eams are over now and I can get on with things here (yes I am counting down, can you tell?).
On Friday during the solar eclipse I was in Sheffield on an open day/interview thing and I was initially devastated by the fact it was cloudy when in face the photos actually turned out pretty well. I also took some photos around Sheffield, some of which i have edited some eclipse photos onto.
I then went to Manchester to see my sister and do some shopping. i did take some photos thent oo which will be up in some time. I plan to go back over some of my photos from the last few years soon and edit them all so I can do some photo posts. That's the plan anyway.
I just think everything looks so ominous and apocalyptic here. The sky and clouds didn't