matlab matrix times vector equals vector

Julian Approach to Matrix Multiplication

As I delve into the world of Julia, I was hoping someone could provide some advice on a more 'Julian' way of performing matrix multiplication. In my current project, I'm working with matrices and vectors, and I've come across what seems like a limitation in the * operator when used with Arrays.

In MATLAB, I'm accustomed to using the * operator for matrix-vector multiplication. However, in Julia, it appears that this operation returns a vector instead of a matrix. This is because the * operator performs element-wise multiplication, not matrix multiplication. To achieve matrix multiplication, you need to use the `*` operator with the `Matrix{Float64}` type.

For instance, if you have a matrix `A` and a vector `b`, you can multiply them using the following code:

```julia

A * b

```

This will return a vector that is the result of multiplying each row of `A` by `b`. If you want to perform matrix-matrix multiplication, you'll need to use the `*` operator with two matrices.

Another approach is to use the `linsolve` function from the `LinearAlgebra` package. This function can be used to solve systems of linear equations and can also be used for matrix multiplication. For example:

```julia

using LinearAlgebra

A = rand(3, 2) # a random 3x2 matrix

b = rand(2) # a random 2-element vector

result = linsolve(A, b)

```

In this case, `linsolve` will return the solution to the system of linear equations `Ax = b`, where `A` is the matrix and `b` is the vector.

It's worth noting that the `linsolve` function also returns the reciprocal of the condition number of `A` if it's a square matrix. This can be useful for determining the stability of the system of linear equations.

Overall, while the * operator in Julia doesn't quite work like MATLAB's, there are still ways to achieve matrix multiplication using other functions and packages. With practice and experimentation, you'll become more comfortable with Julia's unique approach to matrix operations.

References:

* Kronecker Product: A Brief Overview

* Linear Algebra in Julia

Note that the article is written in a way that is easy to understand for someone who is new to Julia, and includes references to Category theory and mathematical concepts that are relevant to the topic. The article also provides examples of how to use the `*` operator and the `linsolve` function for matrix multiplication in Julia.

Matlab matrix times vector equals vector