A cross product takes two vectors and produces a vector.Īdding two vectors is equivalent to putting the tail of one vector against.A dot product takes two vectors and produces a scalar.Vector multiplication is more complicated, there is not a general mutiplication that multiplies two vectors and produces another vector, however there are two types of multiplication that combine two vectors and produce another quantity. Vector addition and subtraction is simple in that we just add or subtract corresponding terms. The elements are often numbers but could be any mathematical object provided that it can be added and multiplied with acceptable properties, for example, we could have a vector whose elements are complex numbers. Hopefully this shed more light onto the way R performs multiplication, especially based on the data type.A vector is a set of elements which are operated on as a single object. If we try this again with the order of the data frames reversed, we will get the same answer. This makes sense since we use only the (*) command. R has done element-wise multiplication on the data frames. Now let’s look at the data to see what we have # View the new data framesįinally, let’s multiply df1*df2 and see what happens. So, let’s try this out by making some new data. # ‘*’ only defined for equally-sized data framesĪccording to the error R is providing, we can only multiply data frames of the same size. Here’s the output of the multiplication (i.e., the errors R provides). You may have guessed it already, but these functions will no longer work. Now let’s try our simple element-wise multiplication again. Notice that the class is now ‘ame’ instead of ‘matrix’ or ‘numeric’.

Here’s the output of those the data type. c1Īnd just to be thorough, let’s check the R data type, to make sure they are not matrices. This is just a feature of the data frame output in R, where it is counting the rows 1 through 3.

Note that there is an extra column of numbers from 1 to 3 for both c1 and x1. Let’s convert our matrices to data frames using the function ame. ***For more info about this see my post here titled CBIND2*** Remember data frames in R can hold different types of data (numbers, letters, etc.), while matrices can only have one type of data. Let’s see what happens when we perform multiplication on data frames. Now, let’s say your data is in a data frame rather than a matrix. This also shows us our 1×3 matrix or vector has the R data type ‘numeric’ and also has the formatting of ‘double’. This shows us that our matrix c, has the R data type of a matrix, with formatting of ‘double’, which means that is is numbers (as opposed to something like ‘character’). We can confirm this using the command class and typeof below: # Get the data type The previous operations were done using the default R arrays, which are matrices. For the matrix multiplication to work, the number of columns in the first matrix (c = 3 columns) has to be equal to the number of rows in the second matrix (x= 1 row). R gives us an error because you can’t multiply a 3×2 and 1×3 matrix. # Error in c %*% x : non-conformable arguments

Now let’s try this with x and c reversed. It will have the same number of rows as the first matrix (x has 1 row) and the same number of columns as the second matrix (c has 2 columns). If you dig back and remember your matrix multiplication, you’ll find that a 1×3 matrix times a 3×2 matrix gives a 1×2 matrix. In R percent signs combined with asterisks are used for matrix multiplication (%*%). #View our element-wise multiplication output We can see that the output of c*x and x*c are the same, and the vector x doubles matrix c. This is where the elements in the same row are multiplied by one another. In R the asterisk (*) is used for element-wise multiplication. If we look at the output (c and x), we can see that c is a 3×2 matrix and x is a 1×3 matrix (which I will also call a vector). First let’s make some data: # Make some data We’re considering element-wise multiplication versus matrix multiplication. This is a basic post about multiplication operations in R.

Multiply a scalar to one vector code