Matrix Dot Product Khan Academy

30 May, 2021

So if you did matrix 1 times matrix 2 then b must equal c in dimensions. Defining and understanding what it means to take the product of a matrix and a vectorWatch the next lesson.

The Dot Product Video Electric Motors Khan Academy

In the image below taken from Khan Academys excellent linear algebra course each entry in Matrix C is the dot product of a row in matrix A and a column in matrix B.

Matrix dot product khan academy. We write the dot product with a little dot between the two vectors pronounced a dot b. Matrix multiplication relies on dot product to multiply various combinations of rows and columns. Khan Academy One of the most important operations involving matrices is the multiplication of two matrices.

If we break this down factor by factor the first two are and. Computing the dot product. Heres a great explanation from Khan Academy of how to compute the dot productwell get to why this is so useful in a little bit.

As it is advanced content I recommend that you check out this Khan Academy article on matrix multiplication. These are the magnitudes of and so the dot product takes into account how long vectors are. Determining the projection of a vector on s lineWatch the next lesson.

If you had matrix 1 with dimensions axb and matrix 2 with cxd then it depends on what order you multiply them. Example of taking the product of two matricesWatch the next lesson. To multiply matrices they need to be in a certain order.

Commonly when we work with Gradient Descent. Kind of like subtraction where 2-3 -1 but 3-21 it changes the answer. Definitions of the vector dot product and vector lengthWatch the next lesson.

This tells us the dot product has to do. Looking at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each otherWatch the next lesson. The final factor is where is the angle between and.

Dot and Cross Product ComparisonIntuitionWatch the next lesson. Weve learned a good bit about the dot product the dot product but when I first introduced it I mentioned that this is only one type of vector multiplication and the other type is the cross product which are probably familiar with from your vector calculus course or from your physics course the cross product but the cross product is actually much more limited than the dot product its useful. Image by Khan Academy The dot product is widely used in Machine Learning when we need to work directly with the arrays.

Dot Product Source. Introduction to the cross productWatch the next lesson. For a matrix product of matrices.

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