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  • By now, I'm sure you know

    現在,我相信你已經知道了。

  • that in just about anything you do in life,

    在你生活中做的任何事情中。

  • you need numbers.

    你需要數字。

  • In particular, though,

    特別是,雖然。

  • some fields don't just need a few numbers,

    有些資料欄不只需要幾個數字。

  • they need lots of them.

    他們需要很多的人。

  • How do you keep track of all those numbers?

    你是如何記錄所有這些數字的?

  • Well, mathematicians dating back

    數學家們可以追溯到

  • as early as ancient China

    早在中國古代

  • came up with a way to represent

    想出了一個方法來代表

  • arrays of many numbers at once.

    同時有許多數字的數組。

  • Nowadays we call such an array a "matrix,"

    現在我們把這樣的數組稱為"矩陣,&quot。

  • and many of them hanging out together, "matrices".

    和很多人一起出去玩,"矩陣"。

  • Matrices are everywhere.

    矩陣無處不在。

  • They are all around us,

    它們就在我們身邊。

  • even now in this very room.

    即使現在在這個房間裡,

  • Sorry, let's get back on track.

    對不起,讓我們回到正軌。

  • Matrices really are everywhere, though.

    不過,矩陣真的無處不在。

  • They are used in business,

    它們被用於商業。

  • economics,

    經濟學;

  • cryptography,

    密碼學。

  • physics,

    物理學;

  • electronics,

    電子產品。

  • and computer graphics.

    和計算機圖形學。

  • One reason matrices are so cool

    矩陣如此酷的原因之一

  • is that we can pack so much information into them

    是我們可以把這麼多的資訊裝進他們的體內

  • and then turn a huge series of different problems

    然後把一大堆不同的問題

  • into one single problem.

    變成一個單一的問題。

  • So, to use matrices, we need to learn how they work.

    所以,要使用矩陣,我們需要學習矩陣的工作原理。

  • It turns out, you can treat matrices

    原來,你可以把矩陣處理成

  • just like regular numbers.

    就像普通數字一樣。

  • You can add them,

    你可以添加他們。

  • subtract them,

    減去它們。

  • even multiply them.

    甚至乘以它們。

  • You can't divide them,

    你不能把它們分開。

  • but that's a rabbit hole of its own.

    但這'是自己的兔子洞。

  • Adding matrices is pretty simple.

    添加矩陣非常簡單。

  • All you have to do is add the corresponding entries

    您所要做的就是添加相應的條目。

  • in the order they come.

    按照他們來的順序。

  • So the first entries get added together,

    所以第一條就被加在一起。

  • the second entries,

    第二條。

  • the third,

    第三個。

  • all the way down.

    一路下來。

  • Of course, your matrices have to be the same size,

    當然,你的矩陣必須是相同的大小。

  • but that's pretty intuitive anyway.

    但無論如何,這'很直觀。

  • You can also multiply the whole matrix

    您也可以將整個矩陣乘以

  • by a number, called a scalar.

    由一個數字,稱為標量。

  • Just multiply every entry by that number.

    只需將每個條目乘以這個數字。

  • But wait, there's more!

    但是,等一下,還有更多!

  • You can actually multiply one matrix by another matrix.

    實際上你可以用一個矩陣乘以另一個矩陣。

  • It's not like adding them, though,

    不過,它'並不像添加它們。

  • where you do it entry by entry.

    你在哪裡逐條做。

  • It's more unique

    它更獨特

  • and pretty cool once you get the hang of it.

    一旦你掌握了訣竅,就會變得非常酷。

  • Here's how it works.

    這裡'是如何工作的。

  • Let's say you have two matrices.

    讓我們'說你有兩個矩陣。

  • Let's make them both two by two,

    讓我們'讓他們兩兩相爭。

  • meaning two rows by two columns.

    意思是兩行兩列。

  • Write the first matrix to the left

    將第一個矩陣寫在左邊

  • and the second matrix goes next to it

    而第二個矩陣就在它旁邊

  • and translated up a bit,

    並翻譯了一下。

  • kind of like we are making a table.

    有點像我們在做一張桌子。

  • The product we get when we multiply the matrices together

    我們將矩陣相乘後得到的乘積。

  • will go right between them.

    會在他們之間進行。

  • We'll also draw some gridlines to help us along.

    我們'也會畫一些網格線來幫助我們。

  • Now, look at the first row of the first matrix

    現在,看看第一個矩陣的第一行。

  • and the first column of the second matrix.

    和第二矩陣的第一列。

  • See how there's two numbers in each?

    看到每個人都有兩個數字了嗎?

  • Multiply the first number in the row

    乘以行中的第一個數字

  • by the first number in the column:

    由列中的第一個數字。

  • 1 times 2 is 2.

    1乘以2就是2。

  • Now do the next ones:

    現在做下一個。

  • 3 times 3 is 9.

    3乘以3是9。

  • Now add them up:

    現在把它們加起來。

  • 2 plus 9 is 11.

    2加9是11。

  • Let's put that number in the top-left position

    讓我們把這個數字放在左上角的位置。

  • so that it matches up with the rows and columns

    以使其與行和列相匹配

  • we used to get it.

    我們曾經得到它。

  • See how that works?

    看到了嗎?

  • You can do the same thing to get the other entries.

    你可以做同樣的事情來獲得其他條目。

  • -4 plus 0 is -4.

    -4加0就是-4。

  • 4 plus -3 is 1.

    4加-3是1。

  • -8 plus 0 is -8.

    -8加0就是-8。

  • So, here's your answer.

    所以,這就是你的答案。

  • Not all that bad, is it?

    也不至於那麼糟糕吧?

  • There's one catch, though.

    不過有一個問題。

  • Just like with addition,

    就像用加法一樣。

  • your matrices have to be the right size.

    你的矩陣必須是正確的大小。

  • Look at these two matrices.

    看看這兩個矩陣。

  • 2 times 8 is 16.

    2乘以8是16。

  • 3 times 4 is 12.

    3乘以4是12。

  • 3 times

    3次

  • wait a minute,

    等一下

  • there are no more rows in the second matrix.

    在第二個矩陣中沒有更多的行。

  • We ran out of room.

    我們沒有房間了。

  • So, these matrices can't be multiplied.

    所以,這些矩陣是不能相乘的'。

  • The number of columns in the first matrix

    第一個矩陣中的列數

  • has to be the same as the number of rows in the second matrix.

    必須與第二個矩陣的行數相同。

  • As long as you're careful

    只要你小心

  • to match up your dimensions right, though,

    以配合你的尺寸,雖然。

  • it's pretty easy.

    這很容易。

  • Understanding matrix multiplication

    瞭解矩陣乘法

  • is just the beginning, by the way.

    對了,這只是個開始。

  • There's so much you can do with them.

    有'的這麼多,你可以做他們。

  • For example, let's say you want

    例如,讓我們說你想

  • to encrypt a secret message.

    加密密文。

  • Let's say it's "Math rules".

    比方說是'的"數學規則"。

  • Though, why anybody would want to keep this a secret

    不過,為什麼有人要保守這個祕密呢?

  • is beyond me.

    是超越我。

  • Letting numbers stand for letters,

    讓數字代表字母。

  • you can put the numbers in a matrix

    你可以把這些數字放在一個矩陣中

  • and then an encryption key in another.

    然後在另一個加密密鑰。

  • Multiply them together

    將它們相乘

  • and you've got a new encoded matrix.

    你就得到了一個新的編碼矩陣。

  • The only way to decode the new matrix

    解碼新矩陣的唯一方法

  • and read the message

    並閱讀資訊

  • is to have the key,

    是擁有鑰匙。

  • that second matrix.

    這第二個矩陣。

  • There's even a branch of mathematics

    甚至還有一個數學分支。

  • that uses matrices constantly,

    不斷使用矩陣的。

  • called Linear Algebra.

    稱為線性代數。

  • If you ever get a chance to study Linear Algebra,

    如果你有機會學習線性代數。

  • do it, it's pretty awesome.

    做到這一點,它'是相當不錯的。

  • But just remember,

    但只要記住。

  • once you know how to use matrices,

    一旦你知道如何使用矩陣。

  • you can do pretty much anything.

    你可以做幾乎任何事情。

By now, I'm sure you know

現在,我相信你已經知道了。

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B1 中級 中文 TED-Ed 矩陣 數字 條目 代數 線性

【TED-Ed】如何建置矩陣,矩陣如何相加,相乘(How to organize, add and multiply matrices - Bill Shillito)

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    Why Why 發佈於 2013 年 03 月 28 日
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