How to Multiply a Matrix by a Vector in MATLAB: Tips and Tricks

When working with matrices and vectors in MATLAB, it's essential to understand the proper way to multiply them together. One common mistake that many users make is to treat 1xN matrices as N-element vectors, which can lead to unexpected results.

In MATLAB, matrix multiplication is performed using the asterisk (*) operator. However, when multiplying a matrix by a vector, you need to use the backslash (\) operator instead. This is because MATLAB treats the vector as a column vector, and the backslash operator performs a linear system solution rather than a dot product.

For example, if you have a matrix A and a vector v, you can multiply them together using the following syntax:

```

w = A \ v;

```

This will give you the result of multiplying the columns of A by v and summing the products.

Another common mistake is to use the dot operator (.) instead of the backslash operator. The dot operator performs an element-wise multiplication, which is not what you want when multiplying a matrix by a vector.

It's also important to note that MATLAB has an optimized implementation of matrix multiplication, which can take advantage of the properties of the matrices involved. This means that even if you use the correct syntax, you may still get faster results than expected.

In addition to the backslash operator, there are several other ways to multiply a matrix by a vector in MATLAB. For example, you can use the `*` operator with the `.` operator to perform an element-wise multiplication:

```

w = A .* v;

```

This will give you the result of multiplying each element of A by the corresponding element of v.

You can also use the `bsxfun` function to broadcast the vector onto the matrix, allowing you to multiply a row or column vector by a larger matrix:

```

w = bsxfun(@times, A, v);

```

This will give you the result of multiplying each element of A by the corresponding element of v, with the vector replicated along the appropriate dimensions.

In conclusion, when working with matrices and vectors in MATLAB, it's essential to use the correct syntax for matrix multiplication. The backslash operator is the most common way to multiply a matrix by a vector, but there are several other ways to do so using various operators and functions. By understanding these different methods, you can take full advantage of MATLAB's optimized implementation of matrix multiplication and get the results you need for your applications.

Multiply matrix by vector matlab