In mathematics, a matrix (plural ma

In mathematics, a matrix (plural matrices) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is treated in certain prescribed ways. One such way is to state the order of the matrix. For example, the order of the matrix below is 2x3, because there are two rows and three columns. The individual items in a matrix are called its elements or entries.

Provided that they are the same size (have the same number of rows and the same number of columns), two matrices can be added or subtracted element by element. The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second. A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f(x) = 4x. For example, the rotation of vectors in three dimensional space is a linear transformation which can be represented by a rotation matrix R: if v is a column vector (a matrix with only one column) describing theposition of a point in space, the product Rv is a column vector describing the position of that point after a rotation. The product of two transformation matrices is a matrix that represents the composition of two linear transformations. Another application of matrices is in the solution of systems of linear equations. If the matrix is square, it is possible to deduce some of its properties by computing itsdeterminant. For example, a square matrix has an inverse if and only if its determinant is not zero. Insight into the geometry of a linear transformation is obtainable (along with other information) from the matrix's eigenvalues and eigenvectors.
Applications of matrices are found in most scientific fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to project a 3-dimensional image onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search.[5] Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions

ผลลัพธ์ (อังกฤษ) 2:

In mathematics, a matrix (plural matrices) is a rectangular array-of numbers, symbols, or expressions, arranged in rows and columns-that is treated in certain prescribed ways. One such way is to state the order of the matrix. For example, the order of the matrix below is 2x3, because there are two rows and three columns. Called the individual items are in a Matrix Elements or its entries. Provided that they are the Same Size (have the Same Number of rows and the Same Number of Columns), Two Can be added or subtracted matrices element by element. The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second. A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f (x) = 4x. For example, the rotation of vectors in three dimensional space is a linear transformation which can be represented by a rotation matrix R: if v is a column vector (a matrix with only one column) describing theposition of a point in space, the product Rv. is a column vector describing the position of that point after a rotation. The product of two transformation matrices is a matrix that represents the composition of two linear transformations. Another application of matrices is in the solution of systems of linear equations. If the matrix is square, it is possible to deduce some of its properties by computing itsdeterminant. For example, a square matrix has an inverse if and only if its determinant is not zero. Insight Into the Geometry of a linear Transformation is obtainable (along with Other information) from the Matrix's eigenvalues ​​and eigenvectors. Applications of matrices are Found in Most Scientific Fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to project a 3-dimensional image onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search. [5] Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions.

ผลลัพธ์ (อังกฤษ) 3:

In, mathematics a matrix (plural matrices) is a rectangular array - of numbers symbols or expressions,,, in arranged rows. And columns - that is treated in certain prescribed ways. One such way is to state the order of the matrix. For example the,, Order of the matrix below is 2x3 because there, are two rows and three columns. The individual items in a matrix are called. Its elements or entries.

.Provided that they are the same size (have the same number of rows and the same number of columns), two matrices can be. Added or subtracted element by element. The rule for, matrix multiplication however is that, two matrices can be multiplied. Only when the number of columns in the first equals the number of rows in the second.A major application of matrices is to represent transformations linear, is that, of generalizations linear functions such. As f (x) = 4x. For example the rotation, of vectors in three dimensional space is a linear transformation which can be represented. By a rotation matrix R: if V is a column vector (a matrix with only one column) describing theposition of a point, in spaceThe product Rv is a column vector describing the position of that point after a rotation. The product of two transformation. Matrices is a matrix that represents the composition of two linear transformations. Another application of matrices is in. The solution of systems of linear equations. If the matrix is square it is, possible to deduce some of its properties by. Computing itsdeterminant.For example a square, matrix has an inverse if and only if its determinant is not zero. Insight into the geometry of a. Linear transformation is obtainable (along with other information) from the matrix 's eigenvalues and eigenvectors.
Applications. Of matrices are found in most scientific fields. In every branch of physics including classical, mechanics optics electromagnetism,,,Quantum mechanics and quantum, electrodynamics they are, used to study, physical phenomena such as the motion of rigid. Bodies. In computer graphics they are, used to project a 3-dimensional image onto a 2-dimensional screen. In probability. Theory and statistics stochastic matrices, are used to describe sets of probabilities; for, instanceThey are used within the PageRank algorithm that ranks the pages in a Google search. [] Matrix 5 calculus generalizes classical. Analytical notions such as derivatives and exponentials to higher dimensions

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