Mathematical notation to multiply matrix elements

In summary, the conversation is about finding the mathematical notation to multiply matrices A and B to produce matrix C, using a componentwise or Hadamard product. The conversation also mentions potentially using common mathematical operators, such as inverse, transpose, dot product, and cross product, to compute this multiplication. The goal is to use this notation in a homework assignment in Mathcad to calculate power requirements for a car at different speeds. It is suggested to use .* instead of * in Matlab for this type of multiplication.
  • #1
DyslexicHobo
251
0
Hi all,

I need to figure out the mathematical notation to multiply matricies A and B = C so that...

If matrix A is...
a1
a2
a3
a4
a5

and matrix B is...
b1
b2
b3
b4
b5

so that matric C is...
a1*b1
a2*b2
a3*b3
a4*b4
a5*b5

Would this involve using a the transverse of a matrix?

Thanks.
 
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  • #2
Looks like the componentwise multiplication of vectors to me.
 
  • #3
That is, the dot product of two vectors.
 
  • #4
When I calculate the doct product of those two matricies, won't I get a single scalar value?
 
  • #5
Okay, I found what I was looking for. It's called a Hadamard product. The Hadamard product A and B produces matrix C so that C_i,j = A_i,j * B_i,j.

Is there any way to compute this using common mathematical operators (such as inverse, transpose, dot product, cross product)?

The reason I ask is because I'm doing a homework assignment in Mathcad calculating power requirements of a car at certain speeds. I'm just assigning the speeds to a single-column matrix and the resistant forces to a single-column matrix. I want to output a power matrix.

If I can't figure it out, I'll just have to manually assign a force and velocity variable to each speed, but there must be a way to do this more easily.
 
  • #6
I don't know what Mathcad is, but in Matlab you would write this sort of multiplication as .* instead of just *. (That last period just ends the sentence of course).
 

1. What is mathematical notation for multiplying matrix elements?

The mathematical notation for multiplying matrix elements is using the multiplication symbol between the two matrices, such as A*B or AB. Alternatively, the dot product notation can also be used, such as A·B.

2. How do you multiply matrices using mathematical notation?

To multiply matrices using mathematical notation, you need to make sure that the number of columns in the first matrix matches the number of rows in the second matrix. Then, you multiply each element in the first row of the first matrix by the corresponding element in the first column of the second matrix and add the products together. This process is repeated for each row and column, resulting in a new matrix with the appropriate dimensions.

3. What is the order of operations for multiplying matrices using mathematical notation?

The order of operations for multiplying matrices using mathematical notation is from left to right. This means that if you have multiple matrices to multiply, you should start with the leftmost matrix and work your way towards the right. This ensures that the dimensions of each matrix are compatible for multiplication.

4. Can you use different mathematical notations to multiply matrices?

Yes, there are different mathematical notations that can be used to multiply matrices, such as the asterisk symbol (*), the dot product notation (·), and the cross product notation (×). It is important to note that while the notation may differ, the process of multiplying matrices remains the same.

5. Are there any rules for using mathematical notation to multiply matrix elements?

Yes, there are a few rules to keep in mind when using mathematical notation to multiply matrix elements. These include making sure that the dimensions of the matrices are compatible (i.e. the number of columns in the first matrix must match the number of rows in the second matrix), and remembering the order of operations (left to right). It is also important to note that the order in which the matrices are multiplied can affect the outcome, as matrix multiplication is not commutative.

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