2,1],[3,7,3],[4,5,4]] by 2 along the x dimension and 0.5 along the y dimension. Rotate [[1,2,1],[3,7,3],[4,5,4]]
Scale [[1,2,1],[3,7,3],[4,5,4]] by 2 along the x dimension and 0.5 along the y dimension.
Rotate [[1,2,1],[3,7,3],[4,5,4]] by 90 degrees around the x dimension
Scaling a matrix means multiplying each element of the matrix by a constant scalar value. This scalar value can be different for each element, or it can be the same value for all elements. Scaling is used to change the size of a matrix, or to stretch or compress its dimensions along one or more axes.
For example, to scale a matrix [[1,2,1],[3,7,3],[4,5,4]] by a factor of 2 along the x dimension and 0.5 along the y dimension, we would multiply the first and third rows by 2, and the second row by 0.5.
Rotating a matrix means changing the orientation of its elements by rotating it around one or more axes. There are different types of rotations, such as rotation around the x, y, or z axis, or a combination of these rotations.
For example, to rotate a matrix [[1,2,1],[3,7,3],[4,5,4]] by 90 degrees around the x dimension, we would first transpose the matrix, then reverse the order of its rows. This would result in a new matrix that is rotated by 90 degrees around the x axis.
Scaling and rotating matrices are important operations in various applications of linear algebra, such as computer graphics, signal processing, and machine learning. They are used to transform images, sound signals, and other data types in order to extract useful features or to prepare them for further analysis.
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