 ## 字幕列表 影片播放

• 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&quot;矩陣，&quot。

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

和很多人一起出去玩，&quot;矩陣&quot;。

• 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&#39;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&#39;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&#39;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&#39;是如何工作的。

• Let's say you have two matrices.

讓我們&#39;說你有兩個矩陣。

• Let's make them both two by two,

讓我們&#39;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&#39;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。

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&#39;。

• 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&#39;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&#39;的&quot;數學規則&quot;。

• 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&#39;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

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