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In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as possible. There are three types of elementary row operations:
Matrix most commonly refers to:
Skin is the layer of usually soft, flexible outer tissue covering the body of a vertebrate animal, with three main functions: protection, regulation, and sensation.
The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring Keanu Reeves, Laurence Fishburne, Carrie-Anne Moss, Hugo Weaving and Joe Pantoliano, and depicts a dystopian future in which humanity is unknowingly trapped inside the Matrix, a simulated reality that intelligent machines have created to distract humans while using their bodies as an energy source. When computer programmer Thomas Anderson, under the hacker alias "Neo", uncovers the truth, he joins a rebellion against the machines along with other people who have been freed from the Matrix.
In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the row vector transpose of More generally, a Hermitian matrix is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of
In linear algebra, the identity matrix of size is the square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1.
In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.
Electrology is the practice of electrical hair removal to permanently remove human hair from the body. Electrolysis is the actual process of removing hair using electricity.
In linear algebra, an n-by-n square matrix A is called invertible if there exists an n-by-n square matrix B such thatwhere In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix.
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements is sometimes referred to as the sparsity of the matrix.
The Matrix is an American cyberpunk media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels, The Matrix Reloaded, The Matrix Revolutions, and The Matrix Resurrections (2021). The first three films were written and directed by the Wachowskis and produced by Joel Silver. The screenplay for the fourth film was written by Lana Wachowski, David Mitchell and Aleksandar Hemon, was directed by Lana Wachowski, and was produced by Grant Hill, James McTeigue, and Lana Wachowski. The franchise is owned by Warner Bros., which distributed the films along with Village Roadshow Pictures. The latter, along with Silver Pictures, are the two production companies that worked on the first three films.
The dermis or corium is a layer of skin between the epidermis and subcutaneous tissues, that primarily consists of dense irregular connective tissue and cushions the body from stress and strain. It is divided into two layers, the superficial area adjacent to the epidermis called the papillary region and a deep thicker area known as the reticular dermis. The dermis is tightly connected to the epidermis through a basement membrane. Structural components of the dermis are collagen, elastic fibers, and extrafibrillar matrix. It also contains mechanoreceptors that provide the sense of touch and thermoreceptors that provide the sense of heat. In addition, hair follicles, sweat glands, sebaceous glands, apocrine glands, lymphatic vessels, nerves and blood vessels are present in the dermis. Those blood vessels provide nourishment and waste removal for both dermal and epidermal cells.
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix
In linear algebra, an eigenvector or characteristic vector is a vector that has its direction unchanged by a given linear transformation. More precisely, an eigenvector, , of a linear transformation, , is scaled by a constant factor, , when the linear transformation is applied to it: . It is often important to know these vectors in linear algebra. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor .
Natural fibers or natural fibres are fibers that are produced by geological processes, or from the bodies of plants or animals. They can be used as a component of composite materials, where the orientation of fibers impacts the properties. Natural fibers can also be matted into sheets to make paper or felt.
In cellular biology, mechanotransduction is any of various mechanisms by which cells convert mechanical stimulus into electrochemical activity. This form of sensory transduction is responsible for a number of senses and physiological processes in the body, including proprioception, touch, balance, and hearing. The basic mechanism of mechanotransduction involves converting mechanical signals into electrical or chemical signals.
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
Anagen effluvium is the pathologic loss of anagen or growth-phase hairs. Classically, it is caused by radiation therapy to the head and systemic chemotherapy, especially with alkylating agents.
Pili bifurcati is characterized by bifurcation found in short segments along the shafts of several hairs, with each branch of the bifurcation being covered with its own cuticle.
"With the Wind and the Rain in Your Hair" is a song composed by Clara Edwards, with lyrics by Jack Lawrence. First published in 1930, it became a hit a decade later.
References
- ↑ James, William; Berger, Timothy; Elston, Dirk (2005) Andrews' Diseases of the Skin: Clinical Dermatology (10th ed.). Saunders. Page 8. ISBN 0-7216-2921-0.
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