237) to see the variable dimensionsī) use the 'Workspace' tab next to the Command Window to see the variable dimensions.Įxample - Problems with Element-wise Matrix Math To check whether the matrices are the same dimensions, you can:Ī) use the who command (FD, p. For example, a 2x3 matrix requires another 2x3 (not a 3x2 or any other size!) matrix in order to perform this type of operation. In order to perform such element-wise operations, each matrix must be the exact same size. For multiplication and division, this means that I can multiply or divide each element of an MxN matrix by the corresponding element of another matrix. It's possible to perform multiplication, division and exponential functions on matrices on an elementwise basis. This example will create a square matrix (the only kind that can be inverted), then invert it.įor more (and better) information, I recommend a book on linear algebra and matrix math, such as the already-mentioned Elementary Linear Algebra by Howard Anton (Drexel University, John Wiley & Sons, 1987). To calculate the inverse of a matrix, simply use the exponent (^) function and take the matrix to the power of -1.Įxample - Calculating the Inverse of a Matrix

Topic 3.5.4.3: Calculating the Inverse of a Matrix Note that this result is the same as above. I'll show this by showing the intermediate step of calculating the inverse of the matrix y. Instead, what Freemat has done is to take the inverse of y, then multiplied that by x. Yes, it seems as if I'm dividing one matrix, x, by another matrix, y. Clear as mud? Let's look at an example.Įxample - Multiplying a Matrix by the Inverse of Another Matrix If it meets these two criteria, then Freemat performs the inverse operation and multiplies the inverse by the first matrix. In order for it to be invertible, the determinant of the matrix cannot be zero. But if the matrix is not invertible, the multiplication operation will not be possible. The method to 'divide' one matrix by another is to first take its inverse, then multiply the inverse. A 2x3 matrix or a 3x2 matrix would not be allowed.Ģ. This means only 2x2, 3x3, 4x4, etc, matrices are allowed. This means they have to have the same number of rows as they do columns (and vice-versa). In order for this process to work, the dividing matrix must have certain properties. This is a case of one matrix being multiplied by the inverse of the other. But this is not a case of dividing one matrix by another.

You might say, 'But in Freemat, I can create two matrices, then divide one by the other.' Yes. This means that you cannot, technically, divide one matrix by another. Topic 3.5.4.2: Dividing a Matrix by Another Matrixĭare I say it? There is no such thing as matrix division. This is an example of element-wise math since each element is divided individually.Įxample - Dividing a Matrix by a Single Number This simply divides each element of the matrix by the single number. You can divide a matrix by a single number, either real or imaginary. Topic 3.5.4.1: Dividing a Matrix by a Single Number

The reason is that, if the two variables represent signals, then this type of element-wise multiplication is the same as mixing the two signals. Personally, this is one of my most-used operations.

Execute a script in freemat