Inverse of a Matrix

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Inverse of a Matrix

For a given square matrix A = ǀǀa_ijǀǀⁿ₁ of order n there exists a matrix B = ǀǀb_ijǀǀⁿ₁ of the same order (called inverse matrix) such that AB = E, where E is the unit matrix; then the equation BA = E also holds. The inverse of a matrix A is designated as A^–1. For the existence of the inverse of a matrix A^–1, it is necessary and sufficient that the determinant of the given matrix A be nonzero; that is, the matrix A must be nonsingular. The elements b_ij of the inverse of a matrix are found by the formula b_ij = A_ji/D, where A_ji is the cofactor of the element a_ij of matrix A and D is the determinant of matrix A.

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No references found			4) We refer the reader to [1] for the definition and the properties of the Moore-Penrose inverse of a matrix. Recovery of missing samples in oversampling formulas for band limited ... by Del Prete, Vincenza / Sampling Theory in Signal and Image Processing Secondary school teachers may use this activity to consolidate their students' learning of certain concepts of matrices such as the algorithm for matrix multiplication and the concept of the multiplicative inverse of a matrix. Harry Potter and the cryptography with matrices by Chua, Boon Liang / Australian Mathematics Teacher			Inverse Function inverse function theorem inverse hour inverse hyperbolic cosecant inverse hyperbolic cosine inverse hyperbolic cotangent Inverse Hyperbolic Function inverse hyperbolic secant inverse hyperbolic sine inverse hyperbolic tangent inverse image inverse implication inverse kinematics inverse latitude inverse limiter inverse logarithm inverse magnetostriction Inverse Magnetron Gauge inverse matrix inverse Mercator chart inverse Mercator projection inverse micelle inverse multiplexor inverse network inverse neutral telegraph transmission Inverse of a Matrix Inverse of a Theorem inverse operator inverse parallel inverse peak voltage inverse piezoelectric effect inverse points inverse probability principle inverse problem inverse ranks inverse ratio inverse relation inverse rhumb line inverse scattering theory inverse secant inverse segregation inverse sine inverse Stark effect inverse substitution inverse tangent Inverse Trigonometric Function inverse variation inverse video inverse voltage inverse Zeeman effect inverse-mapping theorem			inverse limiter Inverse Lithography Technology inverse logarithm inverse magnetostriction Inverse Magnetron Gauge Inverse map Inverse map Inverse mapping Inverse mapping inverse Marcus Gunn syndrome Inverse matrix Inverse Mean Free Path inverse Mercator chart inverse Mercator projection inverse micelle Inverse Modelling of the Atmospheric Chemical Composition Inverse Modified Discrete Cosine Transform Inverse multiplexer Inverse multiplexer Inverse Multiplexing for ATM Inverse Multiplexing over ATM Inverse multiplexor Inverse multiplexor Inverse NAND Flash Translation Layer Inverse Narrow Width Effect inverse network inverse neutral telegraph transmission Inverse of a Matrix Inverse of a Theorem Inverse of Nontangential Proper Part Inverse of Tangential proper part Inverse operation Inverse operation Inverse operator Inverse operator Inverse order Inverse parallel Inverse parallel Inverse parallel inverse peak voltage Inverse Perspective Mapping Inverse photoemission Inverse photoemission spectroscopy Inverse Photopyroelectric inverse piezoelectric effect Inverse Planning by Simulated Annealing Inverse points Inverse points Inverse polymerase chain reaction Inverse population Inverse population Inverse Positioning System Inverse Power Law Inverse Probability of Censoring Weighted Inverse Probability of Treatment Weighted inverse probability principle Inverse problem Inverse Problems, Design and Optimization Symposium

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