Dividing a number by a column matrix in Matlab

For example if I were to type this in matlab: >> 1/[1, 2 ,3] There would be an error: >> Error using / Matrix dimensions must agree.

But if I were to type this in Matlab >> 1/[1; 2; 3] The answer would be: [0 0 0.3333]

Why is Matlab doing this ?

Answer 1

[Aditya]

Hi Duong Cao,

Here's an explanation of this behavior that you're observing:

1] Matrix Division Error:

• When you try 1/[1, 2, 3], MATLAB attempts to perform matrix right division. Here, it interprets the operation as solving the equation x * [1, 2, 3] = 1 for x. This requires the dimensions to be compatible for matrix multiplication, which isn't possible because a scalar (1x1) cannot multiply a row vector (1x3) to produce a scalar (1x1). Hence, you encounter a dimension mismatch error.

2] Pseudo-Inverse Solution:

• When you use 1/[1; 2; 3], MATLAB interprets this as multiplying 1 by the pseudo-inverse of the column vector [1; 2; 3]. This is a valid operation because the pseudo-inverse provides a way to handle non-square matrices, resulting in a least-squares solution. In this case, it returns [0, 0, 0.3333], which satisfies the equation in a least-squares sense.

For more detailed information, you can refer to the MATLAB documentation on matrix right division:

• mrdivide, / : https://www.mathworks.com/help/matlab/ref/double.mrdivide.html

Additionally, you may find this MATLAB Central answer post helpful, as it discusses a similar case:

• https://www.mathworks.com/matlabcentral/answers/386947-when-using-matlab-you-can-actually-divide-a-scalar-by-column-vector-and-produce-a-result-how-does