Suppose we have a subspace \(\mathbb{S}\) of \(\mathbb{R}^n\) whose basis consists of \(k\) vectors \(\vec{v}_1,\vec{v}_2, \ldots , \vec{v}_k\). \[ \mathbb{S ...

Modern applications such as machine learning and large-scale optimization require the next big step, "matrix calculus" and calculus on arbitrary vector spaces. This class covers a coherent approach to ...

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Principal component analysis (PCA) is widely used for data reduction in group independent component analysis (ICA) of fMRI data. Commonly, group-level PCA of temporally concatenated datasets is ...

After performing dimension reduction by SVD, we systematically evaluated the structural and functional implications of additional EVs orthogonal to EV1 ... Here U is a matrix composed of eigenvectors, ...

This course gives a thorough introduction to linear algebra with emphasis on vector spaces, linear maps, spectral theory, orthogonality and applications of this theory. MATLAB is used for ...

Theoretical Physics is aimed at students interested in the more mathematical and theoretical aspect of physics. The course provides a solid grounding in all aspects of physics, both theoretical and ...

Rotations and linear transformations in 2D, 2x2 and 3x3 matrices, eigenvectors and eigenvalues ... Curvilinear coordinates, spherical and cylindrical coordinates, orthogonal curvilinear coordinates, ...