Understanding Matrix Operations: A/C vs. A\C, A./A, and More in MATLAB

[Physics_rocks]

Hi all ,

I'd like your help with some actions taken with matrices .
if A=[1 2 3 ; 4 5 6 ; 7 8 9 ] and C=[1 3 -1 ; 2 4 0 ; 6 0 1 ]

what is the difference between A/C and A\C ?
what does it mean A./A ? what is A. ? MATLAB doesn't give me an answer when I write A.

thanx

 

[matonski]

Think of A/C and A\C as more efficient ways of calculating A*inv(C) and inv(A)*C, respectively.

A. doesn't mean anything. It's ./ that means something. ./ means divide element by element. Adding the . to an operator means to do it element by element. For example A*A is matrix multiplication while A.*A means just multiply the corresponding elements.

 

[oswaler]

I am familiar with matrix operations and their importance in various fields of study. In regards to your question, A/C and A\C are both matrix division operations in MATLAB, but they have different meanings and results.

A/C represents the left division operation, also known as the mldivide operator. This operation is used to solve linear systems of equations, where C represents the coefficients of the equations and A represents the variables. The result of A/C is the solution to the linear system.

On the other hand, A\C represents the right division operation, also known as the mrdivide operator. This operation is used to solve linear systems of equations in a different way, where A represents the coefficients and C represents the variables. The result of A\C is the solution to the linear system in a different form.

Moving on to A./A, this operation represents element-wise division of matrix A by itself. This means that each element in A is divided by its corresponding element in A, resulting in a matrix of ones. This operation is useful in certain mathematical calculations and can also be used to check for equal elements within a matrix.

Lastly, A. is not a valid operation in MATLAB. The dot represents the element-wise operation, which can be used with various mathematical operations such as addition, subtraction, multiplication, and division. However, it cannot be used alone without a specific operation following it.

I hope this helps clarify the differences between A/C, A\C, and A./A in MATLAB. Keep exploring and experimenting with matrix operations to gain a better understanding of their applications in scientific research.