Search results

In mathematics, an '''eigenoperator''', ''A'', of a [[Matrix (mathematics)|matrix]] ''H'' is a [[linear operator]] such that [[Category:Matrix theory]] ...

...ect, and may refer to the dimension of the left [[Nullspace|nullspace of a matrix]], the dimension of the [[cokernel]] of a linear transformation of a [[vect == Left nullspace of a matrix == ...

In [[abstract algebra|algebra]], a '''triangular matrix ring''', also called a '''triangular ring''', is a [[ring (mathematics)|rin ...M,</math> and <math>u\in U,</math> with ordinary [[matrix addition]] and [[matrix multiplication]] as its [[binary operation|operations]]. ...

In [[linear algebra]], two ''n''-by-''n'' [[matrix (mathematics)|matrices]] ''A'' and ''B'' are called '''consimilar''' if ...similar by some real matrix <math>S</math>, consimilarity is the same as [[matrix similarity]]. ...

...[[edge (graph theory)|edge]]s which is incident with each [[vertex (graph theory)|vertex]] exactly once. ...>V = \{1, 2, \dots , n\}</math> then the Tutte matrix is an ''n''-by-''n'' matrix ''A'' with entries ...

{{Short description|Matrix whose eigenvalues have negative real part}} ...|the Hurwitz matrices used to check stability of polynomials|Routh–Hurwitz matrix}} ...

...ed estimate of <math>R_{X}</math>, the <math>N \times N</math> correlation matrix of the array signals, may be obtained by means of a simple [[averaging]] sc ...e matrix|inverse]] of <math>R_{X}</math>, and the inverse of the estimates matrix is then used for finding estimated optimal weights. ...

...|last2=Lewis |first2=A. S. |last3=Overton |first3=M. L. |title=Optimizing matrix stability |url=https://www.ams.org/journals/proc/2001-129-06/S0002-9939-00- ...the ([[real number|real]] or [[complex number|complex]]) eigenvalues of a matrix ''A'' ∈ '''C'''^{''n'' × ''n''}. Then its spectral abscissa is defi ...

...ring]] over any [[commutative ring]]. The notion has an application to the theory of [[polynomial identity ring]]s. *[[Generic matrix ring]] ...

{{Short description|S-matrix causality condition}} ...um field theory]]. The condition was introduced in axiomatic quantum field theory by [[Nikolay Bogolyubov]] in 1955. ...

...be considered as the [[orthogonal projection]] of a larger real symmetric matrix '''A''' onto a linear subspace spanned by the columns of&nbsp;'''B'''. The ...symmetric matrix and '''B''' an ''n''&nbsp;×&nbsp;''r'' [[semi-orthogonal matrix]] such that {{math|'''B'''^T'''B'''}} = {{math|''I''<sub>''r''</s ...

...s|isbn=0898714540|location=Philadelphia|oclc=43662189}}</ref>) is a square matrix ''A'' whose range is equal to the range of its [[conjugate transpose]] ''A' ...+</sup>A''.<ref>{{Cite book|title=Scalar, Vector, and Matrix Mathematics : Theory, Facts, and Formulas.|last=S.|first=Bernstein, Dennis|date=2018|publisher=P ...

...positive, negative, and zero eigenvalues of a block partitioned Hermitian matrix}} ...aynsworth, E. V., "Determination of the inertia of a partitioned Hermitian matrix", ''[[Linear Algebra and its Applications]]'', volume 1 (1968), pages 73–81 ...

...lated definitions. Let {{math|''n''}} equal the number of [[Vertex (graph theory)|vertices]] of the graph. ...graph is defined as the [[Rank (linear algebra)|rank]] of its [[adjacency matrix]]. ...

...]. The layout uses the [[eigenvectors]] of a matrix, such as the [[Laplace matrix]] of the graph, as [[Cartesian coordinate]]s of the graph's vertices. ...(or smallest) eigenvalues and corresponding eigenvectors of the Laplacian matrix of the graph and then use those for actually placing the nodes. ...

{{Short description|Concept in probability theory and machine learning}} ...tropic position''' if its [[covariance matrix]] is equal to the [[identity matrix]]. ...

.... (In some contexts, particularly [[computer science]], the term "Boolean matrix" implies this restriction.) ...ir of elements to obtain the corresponding matrix intersection or union. A matrix is contained in another if each entry of the first is contained in the corr ...

...here every entry is either zero or one) that does not contain any [[Square matrix|square submatrix]] of odd order having all row sums and all column sums equ ...ref><ref name="Schrijver1998">{{cite book|author=Alexander Schrijver|title=Theory of Linear and Integer Programming|url=https://archive.org/details/theorylin ...

...ltiplication]].<ref>{{harvp|Riehl|2016|pages=4-5}}</ref><ref name="perrone-matrix">{{harvp|Perrone|2024|pages=99-100}}</ref> ...imes m</math> [[real number|real]] [[matrix (mathematics)|matrix]], i.e. a matrix with <math>n</math> rows and <math>m</math> columns. ...

...or column and <math>M(R)</math> is its [[ideal (ring theory)|ideal]] of [[matrix (mathematics)|matrices]] having only finitely many nonzero elements. It is ....rutgers.edu/~weibel/Kbook.html The K-book: An introduction to algebraic K-theory]" ...