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PARATHD-01529 Here are some terms and formulas for honing knowledge on matrices, followed by the applications in various fields as per your request. **Titles:** Term and Formula to Master Matrices. **Point-Point:** Following are the terms and formulas for matrices*** What is Matrix:** The matrix is a rectangular array of numbers, which is arranged in rows and columns. These matrices are usually used to solve linear equations. The matrices are generally written in square brackets. *** What is Neat:** It is the numerical value of the matrix, which is usually of a square matrix. It is determined by some specific formulas. For example, 2x2 matrix has a determinant as (ad - bc). *** What is Inverse:** The inverse of a matrix is a matrix that when multiplied with the original matrix gives a identity matrix. If the matrix is non-zero, then the inverse of a matrix can be found. *** What is Eigenvalue:** Eigenvalue is a scalar that is associated with a given linear transformation of an eigenvector. Each eigenvalue always has a corresponding eigenvector. *** What is Linear Transformation:** It is a function from one vector space to another vector which keeps the linearity of the transformed vector. For example, it is a linear transformation from a function to a function. **Here are the formulas to study matrices:**: *** Sum of matrices:** The sum of two matrices is determined by adding up the components of each matrix. For example, [a, b] + [c, d] = [a + c, b + d] *** Product of matrices:** The product of two matrices is determined by multiplying the elements from row one of the first matrix with the components of column two of the second matrix. For example, [a, b] x [c, d] = [ac + bc, ad + bd] *** Determinant of a matrix:** The determinant of a matrix is determined by a special formula. For example, the determinant of matrix [a, b; c, d] is (ad - bc). *** Inverse of a matrix:** The inverse of a matrix is determined by a specific formula. For example, the inverse of matrix [a, b; c, d] is [d, -b; -c, a] / (ad - bc) *** Eigenvalue of a matrix:** The eigenvalue of a matrix is determined by a special formula. For example, the eigenvalues of matrix [a, b, c] are (a - d), (c - d), and (b - d). *** Linear Transformation of a matrix:** The linear transformation of matrix is determined by a special formula. For example, the linear transformation of matrix [a, b, c] is [a + b + c, a - b + c, a + b - c] **Facts:** The matrix generally has three dimensions: row, column, and scalar. A matrix can be utilized to solve linear equations. It can also be used to determine the determinant, inverse, eigenvector, and eigenvalue of a matrix. Following the first segment, let's now turn to the applications of matrices in various fields, ensuring a comprehensive understanding of their significance. **Point-Point:** The important applications of matrices in various fields are as follows:- *** Engineering:** Matrices are widely used in engineering to solve complex problems or equations, such as the simultaneous equation. *** Physics:** Matrices are utilized in physics to calculate the product, determinant, and inverse of a matrix. *** Computer science:** In computer science, matrices are used in coding, software, and even in robotics. *** Graphs:** Matrices are used in graph theory to create a graph, which is then used to solve problems, such as determining the shortest path. *** Statistics:** Matrices are used in statistics to calculate the mean, variance, and standard deviation of a matrix. **Followers:** The matrix is a key concept in mathematics and has applications in various fields. It is needful to understand matrix to correctly solve different problems in different fields. **For:** The formula of several types of matrix is based on the original matrix basis, and their application in different fields is the seventh and eighth section of the matrix. Similarly, the matrix can be used in the fields of physics, computer science, graphs, and statistics as well. **Titles:** Applications of Matrix in Various Fields. As you successfully completed the provided course, you now have a complete knowledge of matrices and it's applications in each field. To make you learn more through these applications and to understand the relation between them, here introduce some book recommendations for you. **Following are the books which you can read to explore matrices:**: *** Linear Algebra and Its Applications.** by D. C. Lay. *** Introduction to Statistics:** by R. M. Swenson. *** Data Science and Robotics:** by S. Kawasaki. *** Physics of Mechanics:** by David Keehan. *** Graph Theory:** by K. Murita. **Ratio:** These books are recommended to get a complete knowledge of matrices and their applications in the respective fields. **Titles:** Books to Study Matrices. </codetable>

11月15日2015年