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Topic: Pseudoinverse

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	Pseudoinverse - Wikipedia, the free encyclopedia
		The pseudoinverse is defined and unique for all matrices whose entries are real or complex numbers.
		The pseudoinverse of the null vector is the transposed null vector.
		If a pseudoinverse is already known for a given matrix, and the pseudoinverse is desired for a related matrix, the pseudoinverse for the related matrix can be computed using specialized algorithms that may need less work.
	en.wikipedia.org /wiki/Pseudoinverse (838 words)

	PlanetMath: pseudoinverse
		Beyond this, pseudoinverses can be defined on any reasonable matrix identity.
		This is version 2 of pseudoinverse, born on 2002-01-04, modified 2006-06-26.
		Object id is 1281, canonical name is Pseudoinverse.
	planetmath.org /encyclopedia/Pseudoinverse.html (106 words)

	Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA ... (Site not responding. Last check: 2007-10-08)
		Pseudoinverse reconstruction of the CLB2 and CLN3 overexpression data in the SVD (a and b) and GSVD (c and d) bases, with the ORFs sorted according to their SVD- and GSVD-phases, respectively.
		Pseudoinverse reconstruction of the CDC15 cell cycle time course mRNA expression data in the SVD (a and b) and GSVD (c and d) cell cycle mRNA expression bases, with the ORFs sorted according to their SVD- and GSVD-phases, respectively.
		Pseudoinverse correlations of the replication initiation proteins’ DNA-binding data with transcription factors’ DNA-binding data, reconstructed in the SVD (a, b, and c) and GSVD (d, e, and f) cell cycle mRNA expression bases.
	intl.pnas.org /cgi/content/full/0406767101/DC1 (1356 words)

	Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA ... (Site not responding. Last check: 2007-10-08)
		Pseudoinverse reconstruction of the proteins' DNA-binding data in the SVD (a and b) and GSVD (c and d) cell cycle mRNA expression bases, with the ORFs sorted according to their SVD- and GSVD phases, respectively.
		Pseudoinverse correlations of the proteins' DNA-binding data with the SVD (a and b) and GSVD (d and e) cell cycle mRNA expression bases.
		Also shown are line-joined graphs of the pseudoinverse correlations with the first (red) and second (blue) eigenarrays that span the SVD-cell cycle expression subspace (b), the third (red), fourth (blue), and fifth (green) arraylets (d), and the 14th (red), 15th (blue), and 16th (green) arraylets that span the GSVD cell cycle expression subspace (e).
	www.pnas.org /cgi/content/full/101/47/16577 (3959 words)

	Manipulator arm position sensing - Patent 4893254
		In the case where the rank of the Jacobian is less than the number of degrees of freedom of the end effector in the particular arm being manipulated the solution of equation (3) minimizes the error in the solution in the least squares sense.
		With the present invention the pseudoinverse is used to determine the joint angle.theta.
		As above indicated because of the error dampled pseudoinverse's ability to move very closely to singular points it is possible for the manipulator to move into alternative solutions and in these types of manipulators suitable precautions should be taken to bias the pseudoinverse to one solution.
	www.freepatentsonline.com /4893254.html (3667 words)

	Matrices
		Your students will use linear regression to fit lines to data in their science classes, so it is nice to see how this is an application of the matrices we've been studying.
		We would use the pseudoinverse to find the values of a, b, and c that minimize SSE in the exact same way.
		For this class, we will just leave them as an example of what can be done in more complicated algebraic structures, and as an example of the applications of matrices to a standard topic in secondary mathematics.
	www.math.ksu.edu /math511/notes/1004.html (1046 words)

	Inverse Kinematics of the Human Arm
		Therefore, a pseudoinverse iteration procedure has to be carried out to tune the joint angles till the correct wrist position is obtained.
		This is the reason Koga et al.[2] have to use the pseudoinverse Jacobian iteration procedure to adjust joint angles.
		Since all the inverse kinematic approaches may produce joint angles which violate their limits, the joint angles corresponding to the swivel angle obtained from the sensorimotor transformation sometimes extend beyond their legal ranges.
	www.isso.uh.edu /publications/A9697/9697-8.html (1868 words)

	Advanced Topic: Matrix Decompositions
		The pseudoinverse has the property that the sum of the squares of all the entries in
		The pseudoinverse found in this way is important, for example, in carrying out fits to numerical data.
		The pseudoinverse is sometimes known as the generalized inverse, or the Moore-Penrose inverse.
	documents.wolfram.com /v4/MainBook/3.7.10.html (439 words)

	Irregular Sampling, Frames and Pseudoinverse (Site not responding. Last check: 2007-10-08)
		It is the purpose of this thesis, to point out the connections between the theory of frames in Hilbert spaces, the theory of pseudoinverse operators and the irregular sampling problem for band-limited functions.
		Projection matrices, mean square solutions and singular value decomposition are used to define the pseudoinverse of a matrix.
		The pseudoinverse (or Moore-Penrose inverse) is a generalization of the ordinary inverse of a matrix.
	www.mat.univie.ac.at /~nuhag/papers/1991/str1191.html (241 words)

	The Receptive-Field Organization of Simple Cells in Primary Visual Cortex of Ferrets under Natural Scene Stimulation -- ... (Site not responding. Last check: 2007-10-08)
		B, The preferred orientation predicted from the spectrum of the regularized pseudoinverse field is plotted against the optimal orientation of sinusoidal grating for 21 simple cells.
		The dotted curve is the spatial-frequency bandpass of the main spectral feature in the two-dimensional Fourier transform of the reverse-correlation map replotted from Figure 3D.
		E, The preferred spatial frequency (SF) predicted from the spectrum of the regularized pseudoinverse field is plotted against the optimal spatial frequency of sinusoidal grating for 18 simple cells.
	www.jneurosci.org /cgi/content/full/23/11/4746 (8432 words)

	Singularity escape/avoidance steering logic for control moment gyro systems - Patent 6917862
		It is emphasized that the singularity-robust inverse of the form (20) is based on the mixed, two-norm and weighted least-squares minimization although the resulting effect is somewhat similar to that of artificially misaligning the commanded control torque vector from the singular vector directions.
		Because the singularity robust steering logic is based on the minimum two-norm, pseudoinverse solution, it does not explicitly avoid singularity encounters but it rather approaches and rapidly transits unavoidable singularities whenever needed.
		The CMG steering logic of this invention is based on the well-known mixed weighted two-norm and least-squares optimization solution with weighting matrices W and V. The proper use of W, in conjunction with the deterministic dither signals in V, eliminates a deficiency of the patented steering logic of Refs.
	www.freepatentsonline.com /6917862.html (6435 words)

	NCAlgebra Homepage: NonCommutative Algebra Software, Examples and Links to other Non commutative computer algebra sites
		PseudoInverse of A,B, and AB does NOT have a finite GB.
		Here is the mathematica file for the pseudoinverse of a column matrix.
		Note that we are solving for the pseudoinverse of a 2x1 matrix with entries a and b where the pseudoinverse is a 1x2 matrix with entries c and d.
	euclid.ucsd.edu /~ncalg (1009 words)

	Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem, ...
		Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem, Brian J. McCartin
		A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem.
		The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.jam/1063629206 (205 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The reason is that a left-invertible matrix has nullspace consisting of zero vector alone, while a matrix with too many columns has more than one vector in its nullspace.
		What you described was an approximation to the Moore-Penrose pseudoinverse; it will be exactly it if you take the limit for Epsilon going to 0 from the right.
		Numerically, this formula (if you settle for the approximate pseudoinverse) suffers from loss of accuracy; it is safer to use RQ-decomposition of a suitably augmented matrix and extract the approximate pseudoinverse from there.
	www.math.niu.edu /~rusin/known-math/98/pseudo_inverse (195 words)

	Inverse and Pseudoinverse Filtering
		Pseudoinverse filtered image with 28682 out of 65536 values of H
		Results of pseudoinverse filtering with threshold value set to minimize frequency content losses.
		More detail of the original image can be determined from the processed image using the Wiener filter implementation.
	www.owlnet.rice.edu /~elec431/projects95/lords/wolf.html (406 words)

	[No title]
		Questions associated with pseudoinverse control are examined in detail and show that in some cases this control leads to undesired arm configurations.
		A method for distributing joint angles of a redundant arm in a good approximation to a true minimax criterion is described.
		Abstract - Control of kinematically redundant manipulators using only pseudoinverse control is known to produce drift in joint space when a cyclic task is performed in rectilinear space.
	www.ece.osu.edu /~klein/webpageabstracts.html (1648 words)

	PseudoInverse Matrix (Not in Base Package) - LabVIEW 8 Help
		PseudoInverse Matrix is the pseudoinverse matrix of the Input Matrix.
		If Input Matrix is square and not singular, then the pseudoinverse is the same as the inverse of a matrix, and the Inverse Matrix VI should be used as a more efficient method of computing the inverse of the Input Matrix.
		Refer to the Linear Algebra Calculator VI in the labview\examples\analysis\linaxmpl.llb for an example of using the PseudoInverse Matrix VI.
	zone.ni.com /reference/en-XX/help/371361A-01/gmath/pseudoinverse_matrix (562 words)

	Block matrix pseudoinverse - Wikipedia, the free encyclopedia
		Block matrix pseudoinverse is a formula of pseudoinverse of a partitioned matrix.
		This is useful for decomposing or approximating many algorithms updating parameters in signal processing, which are based on least squares method.
		If the above matrix is full rank, the pseudoinverse matrices of it and its transpose are as follows.
	en.wikipedia.org /wiki/Block_matrix_pseudoinverse (341 words)

	pseudo inverse matrix calculation - Numerical Recipes Forum
		For non-singular square matrices, the pseudoinverse is equivalent to the standard inverse.
		Using SVD singular value decomposition A=Transpose[u].W.V, it is possible to define a pseudoinverse for non-square matrices A, or for singular square ones.
		The pseudoinverse is defined in SVD terms as
	www.nr.com /forum/showthread.php?t=540 (149 words)

	Pseudoinverse of a Complex Matrix with JAVA
		Comp.DSP -> Pseudoinverse of a Complex Matrix with JAVA
		Or....Can I compute the pseudoinverse of real part and imaginary part of
		the matrix, and then combinate the results to obtain the pseudoinverse of
	www.dsprelated.com /showmessage/60606/1.php (1164 words)

	[No title]
		Klein, ``The Lie Bracket condition as a test of stable, drift-free pseudoinverse trajectories,'' IEEE Trans.
		Klein and B. Kee, ``The Nature of Drift in Pseudoinverse Control of Kinematically redundant Manipulators,'' IEEE Journal of Robotics and Automation, vol.
		Klein and C. Huang, ``Review of pseudoinverse control for use with of kinematically redundant manipulators,'' IEEE Trans on Systems and Man and Cybernetics, vol.
	www.ece.osu.edu /~klein/publications.html (1267 words)

	Linear algebra
		PInverse(mat,tol) returns the pseudoinverse (also called the generalized or Moore-Penrose inverse) of the matrix mat with tolerance tol
		The pseudoinverse equals the inverse when mat is a non-singular (all singular values > 0) square matrix.
		The sum of squares of the elements of mat×PInverse(mat)-I is minimized, where I is the identity matrix, and so the pseudoinverse is useful for data fitting.
	www.ibiblio.org /technicalc/packages/mathtools/linearalgebra.htm (1176 words)

	Derivation of the optimal linear estimator
		The decoding phase is, as before, simply taking the sum of scaled versions of the eigenvectors of the head data set.
		Note that if the observed dimensions of the input head change over time, this pseudoinverse must be recomputed.
		Even if it had to be moved into the reconstruction loop, it would not slow down the system unacceptably (the reconstruction step takes roughly ten seconds, which is roughly the time for the computation of this pseudoinverse).
	xenia.media.mit.edu /~kbrussel/Eigenheads/node10.html (468 words)

	APS - 2005 APS March Meeting - Event - Genomic Signal Processing: Predicting Basic Molecular Biological Principles
		Now we describe an integrative data-driven model, which uses pseudoinverse projection (1).
		\\ \\ The integrative pseudoinverse projection model formulates any number of genome-scale molecular biological data sets in terms of one chosen set of data samples, or of profiles extracted mathematically from data samples, designated the ``basis'' set.
		\\ \\ Mapping genome-scale protein binding data using pseudoinverse projection onto patterns of RNA expression data that had been extracted by SVD and GSVD, a novel correlation between DNA replication initiation and RNA transcription during the cell cycle in yeast, that might be due to a previously unknown mechanism of regulation, is predicted.
	meetings.aps.org /Meeting/MAR05/Event/26892 (370 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		I need to write a code for :the pseudoinverse in C++.
		So if i have it in MATLAB i can :translate it into C++, but as i mentioned it is "hidden" in :MATLAB What version are you referring to?
		I typed "type pinv" and got the following - of course, you need svd which is a built-in function: function X = pinv(A,tol) %PINV Pseudoinverse.
	www.math.niu.edu /~rusin/known-math/01_incoming/pseudoinverse (240 words)

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