Matrix Dimensions must Agree

When I used the following command on MATLAB I got the error

>> D1d = D_pca(:,1)*eigvects(:,1)
Error using  * 
Inner matrix dimensions must agree.

But when I added the ' at the end then the error disappeared.

>> D1d = D_pca(:,1)*eigvects(:,1)'

D1d =

6.1500   -2.0524
-1.9502    0.6508
-8.6987    2.9029
4.4990   -1.5014

I need to help with why this happened? What is the reason behind it? What does the comma do?

Answer 1

[Walter Roberson]

Your D_pca has 4 rows and an unknown number of columns.

Your eigvects has 2 rows and an unknown number of columns.

D_pca(:,1)*eigvects(:,1)

is a request to use algebraic matrix multiplication (inner product) between a 4 x 1 vector and a 2 x 1 vector. But for inner product, the number of columns in the first operand (which is 1 in this case) must match the number of rows in the second operand (which is 2 in this case).

When you ask D_pca(:,1)*eigvects(:,1)' then you are asking to have inner product between a 4 x 1 matrix and transpose of a 2 x 1 vector, which is 4 x 1 * 1 x 2, and then the "inner dimensions" match so you can multiply and produce a 4 x 2 result.