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Similarly, the function det ( A ) 1 / m is concave and the corresponding maximization problem can be phrased in a similar way using a geometric mean bound from Chinese Laundry Womens Exclusive ZHappy Hour Merlot TlFFMwrmI

We next consider a non-square matrix A R m × p . Assume p m and denote the singular values of A by

σ 1 ( A ) σ 2 ( A ) σ p ( A ) 0.

The singular values are connected to the eigenvalues of A T A via

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σ i ( A ) = λ i ( A T A ) ,

and if A is square and symmetric then σ i = | λ i | . We show next how to optimize several functions of the singular values.

Largest singular value

The epigraph σ 1 ( A ) t can be characterized using LakeRom Mens Leather Loafers Shoes Men Slip On Shoes Casual Leather Shoes Black35 9gn8v

A T A t 2 I

which from Schur’s lemma is equivalent to

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[ t I A A T t I ] 0.

The largest singular value σ 1 ( A ) is also called the spectral norm or the 2 -norm of A , A 2 := σ 1 ( A ) .

Daily Titan

In Opinion
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Dear opinion writers:

I bet you thought it would be fun getting to write for the only section of a newspaper that’s allowed to be somewhat biased.

You probably thought the opinion desk was going to be a well-deserved break from the linear, “use the right word or else risk your journalistic integrity” writing and fact-paranoia so common in the rest of the newspaper. Heck, you don’t even need to interview people to write an opinion piece.

But instead, your writing has only fueled a passionate response from a collection of people who don’t read past the headline, would prefer to lazily comment on social media instead of writing a letter to the editor and who accuse you of being the worst journalist in the history of journalism.

The external monologue of the comment section often sounds like this:

“How dare you write an article for the opinion section that’s dripping with your personal opinion? As a journalist, it’s your job to keep your writing in the hands of the goddess ‘Neutrality’ and never comment on current events. Stick to a robotic output of content that doesn’t offend anyone.”

On the other hand, if you can’t manage to stoke the fires of controversy, your nightly prayer to the editorial gods is that your writing gets any reaction and not the dreaded, no notification-inducing article that makes you beg for even a single mad or shocked Facebook reaction. You’d even settle for a patronizing blue thumbs-up.

Then there’s the fact that everyone does indeed have an opinion, so the questions that hover over your keyboard like the quips of a demented Microsoft Office Assistant are: what makes your opinion so goddamn unique? What kind of prolonged, narcissistic, self-aggrandizing ego-trip do you have to be on to write for the opinion desk?

You think you’re special because that’s what your parents have told you your entire life and now it’s translated into your writing, apparently.

Underlying all of this is the question you ask yourself on a regular basis: what’s the point?

Any good opinion writer will tell you that the point is to start a conversation. You do all the research, make your argument, and yes, put your opinion in writing so that someone will respond, and maybe even point out something you missed.

But in the ADIDAS Mens F30 TRX FG High Energy/Wht/Elec 90 M XIuQrBl
, it seems the only way to elicit any response, let alone conversation, is to write outlandish and against-the-grain pieces that make readers angry enough to comment. Controversy breeds very loud opinions.

Just take a look at what happened in the Daily Titan’s opinion section leading up to Anna Vita7 Womens upper inlayed crystal decor PU ankle strap thong sandals Yellow HgWB4oIVg
on campus. The number of Letters to the Editor was unprecedented.

A Wealth of Common Sense

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The following is one of my favorite running stats on the stock market:

Over the years I’ve noticed that whenever these types of long-term numbers are presented there tend to be two extreme responses:

There is some truth in each of these statements, but as with most things the historical data is never black or white, but a shade of gray. The future is uncertain, so investors should always think in terms of probabilities, never guarantees. What this data tells me is that the longer your time horizon, the higher your probability of seeing a gain in the stock market.

Does this mean that you’re guaranteed to earn a certain level of returns in stocks if you hold them for a specfied time frame? No.

Will these same results be guaranteed to repeat themselves in the future? No.

Has anyone figured out a better way of compounding your money in stocks beyond increasing your holding period? Not many.

Are there investors out there who actually have twenty year time horizons? Absolutely — Millennials just starting out in their career, middle-aged workers playing catch-up with their retirement savings and even retirees who will likely have 2-3 more decades to invest during their retirement years. The difference in each case comes down to how much each of these investors should hold in stocks and what their needs are in the meantime.

I like to think that every single retirement contribution has it’s own twenty or thirty year time horizon.

The usual caveats apply here — these numbers are before inflation, taxes or costs are taken into account (although one of the biggest benefits about a longer holding period is that you can reduce the impact of trading costs and taxes on your portfolio). With that disclaimer out of the way, here are a few more interesting long-term stock market stats I found while computing these numbers:

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Full Disclosure: Nothing on this site should ever be considered to be advice, research or an invitation to buy or sell any securities, please see my Terms Conditions page for a full disclaimer.

Now go talk about it.

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Nice post, thanks Ben. One of the remarkable things from reviewing the historical data is that variance of equities is lower than that of bonds (and incredibly low as you pointed out) when the time horizon is expanded (remembering a chart from Jeremy Siegel’s book) due to the mean reverting nature of equities. The hard part I would think is knowing how to reallocate as one moves closer to retirement/withdrawals.

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