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# Rの行列とベクトル計算

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よく使うやつをまとめておく

### データ準備

```> a <- c(2, 5)
> b <- c(3, 7)
> X <- matrix(1:4, nrow=2, ncol=2)
> Y <- matrix(5:8, nrow=2, ncol=2)

> print(a)
[1] 2 5
> print(b)
[1] 3 7
> print(X)
[,1] [,2]
[1,]    1    3
[2,]    2    4
> print(Y)
[,1] [,2]
[1,]    5    7
[2,]    6    8
```

## ベクトル と ベクトル

### ベクトル同士の積（ベクトルの内積） `%*%`

```> print(a %*% b)
[,1]
[1,]   41
```

### ベクトル同士の要素積 `*`

```> print(a * b)
[1]  6 35
```

### ベクトル同士の直積(ベクトルのテンソル積)　`%o%`

```> print(a %o% b)
[,1] [,2]
[1,]    6   14
[2,]   15   35
```

## 行列 と 行列

### 行列同士の積 `%*%`

```> print(X %*% Y)
[,1] [,2]
[1,]   23   31
[2,]   34   46
```

### 行列同士の要素積 `*`

```> print(X * Y)
[,1] [,2]
[1,]    5   21
[2,]   12   32
```

### 行列同士のクロネッカー積 `%x%`

```> print(X %x% Y)
[,1] [,2] [,3] [,4]
[1,]    5    7   15   21
[2,]    6    8   18   24
[3,]   10   14   20   28
[4,]   12   16   24   32
```

## 行列とベクトル

### 行列とベクトルの積 `%*%`

```> X %*% a
[,1]
[1,]   17
[2,]   24
```

### 行列とベクトルの要素積（わかりづらい） `*`

```> X * a
[,1] [,2]
[1,]    2    6
[2,]   10   20
```
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