Matrix by Vector Multiplication in Matlab: Understanding the Basics

When working with matrices and vectors in Matlab, it's essential to understand that a one-dimensional vector (1xN) is not the same as an N-element vector. This distinction can lead to unexpected behavior when performing matrix operations.

For square matrices, Matlab will attempt to solve the linear system of equations. However, for rectangular matrices, it will seek the least squares solution. To perform dot products in Matlab, you can use the built-in `dot` function or resort to a typical linear algebra notation using the backslash operator (`\`). For example:

```matlab

v = rand(1000);

z = v' * w;

```

Alternatively, you can multiply elements of an n-dimensional array on an element-wise fashion using the dot operator. This operator will broadcast the scalar multiplication operator on an element-wise basis.

In addition to these methods, matrix-matrix multiplication can be performed using a Matlab-style syntax:

```matlab

A * B;

```

Matrix and vector multiplication can also be achieved using the `*` operator. Two-dimensional arrays (or matrices) are a fundamental part of Julia programming language. Once you know how to input arrays, it's crucial to understand how to operate with them.

In this tutorial series, we have discussed various ways of performing matrix operations in Julia, including element-wise multiplication and broadcasting scalar multiplication operators. By mastering these concepts, you can efficiently manipulate matrices and vectors in your Matlab code.

Matrix by vector multiplication matlab