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Linear algebra

Last revised by Dr Bahman Rasuli on 08 Jan 2021

Linear algebra is a field of mathematics with extremely diverse applications. This type of mathematics extends arithmetical operations from numbers to complex objects like matrices and vectors.

In terms of radiology, linear algebra applications include CT reconstruction algorithms, neural network algorithms, windowing, and MRI sequence algorithms.  Practically speaking, linear algebra deals with linear equations, matrices and vectors. The vectors of linear algebra should not be confused with vectors as conceptualized in physics or trigonometry.

Linear algebra underlies much of computerized image processing, as all digital images are matrices. All computerized texture analysis and convolutional neural network programs rely on operations on matrices of the image, for example, matrix multiplication inside of their various algorithms.

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