Geophysical Data Analysis: Discrete Inverse Theory: MATLAB Edition (International Geophysics Series) by Menke William

Author:Menke, William [Menke, William]
Language: eng
Format: azw3
ISBN: 9780123977847
Publisher: Elsevier Science
Published: 2012-06-25T16:00:00+00:00

(7.32)

The matrix U is an N × N matrix of eigenvectors that span the data space S(d):

(7.33)

where the u(i)s are the individual vectors. The vectors are orthogonal to one another and can be chosen to be of unit length so that UUT = UTU = I (where the identity matrix is N × N). Similarly, V is an M × M matrix of eigenvectors that span the model parameter space S(m) as

(7.34)

Here the v(i)s are the individual orthonormal vectors so that VVT = VTV = I (the identity matrix being M × M). The matrix Λ is an N × M diagonal eigenvalue matrix whose diagonal elements are nonnegative and are called singular values. In the N = 4, M = 3 case

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