# Linear Algebra Operations on Vectors and Matrices

Multiplying a vector by a scalar works directly, as you saw earlier. Here’s another example:

> y [1] 1 3 4 10 > 2*y [1] 2 6 8 20

If you wish to compute the inner product (or dot product) of two vectors, use `crossprod()`

, like this:

> crossprod(1:3,c(5,12,13)) [,1] [1,] 68

The function computed 1 · 5 + 2 · 12 + 3 · 13 = 68.

Note that the name `crossprod()`

is a misnomer, as the function does not compute the vector cross product. We’ll develop a function to compute real cross products in Section 8.4.1.

For matrix multiplication in the mathematical sense, the operator to use is `%*%`

, not `*`

. For instance, here we compute the matrix product:

Here’s the code:

> a [,1] [,2] [1,] 1 2 [2,] 3 4 > b [,1] [,2] [1,] ...

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