Khan Academy
Learn about matrices, their properties, and how to perform operations with them.
Transpose of a matrix product - Khan Academy
Let's define my matrix C as being equal to the product of A and B. So what are going to be the dimensions of C? Well, an m by n matrix times an n by m matrix, these two have to be equal even for the matrix product to be defined.
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If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Explore. Browse By Standards; Virginia Math. NEW. Grade 6 (Virginia) NEW. ... Matrix determinant gives area of image of unit square under mapping. Matrices as transformations. Matrix from visual representation of transformation ...
Khan Academy
3X3 matrices can define transformations of the 3D space. In this worked example, we see how to find the matrix transformation that is the composition of two other matrices. Created by Sal Khan.
Khan Academy
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Khan Academy
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Khan Academy
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Explore. Search. AI for Teachers. Free. Donate Log in Sign up. Search for courses, skills, and videos. Our mission is to provide a free, world-class education to anyone, anywhere.
Khan Academy
Sal shows how to find the determinant of a 2x2 matrix.
Linear transformations as matrix vector products
If any matrix-vector multiplication is a linear transformation then how can I interpret the general linear regression equation? y = X β. X is the design matrix, β is a vector of the model's coefficients (one for each variable), and y is the vector of predicted outputs for each object. Let's say X is a 100x2 matrix and β is a 2x1.