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A matrix that gives an identity value when you multiply it with its transpose is known as an orthogonal matrix. Similarly, two vectors are said to be orthogonal when they form a right angle or are perpendicular. When you use the concept of matrices to solve these vectors, the result will be a square matrix with an equal number of rows and columns. If the transpose of a square matrix with real elements is equivalent to its inverse matrix, then it is an orthogonal matrix.
Singular Value Decomposition
The term singular value decomposition is used in linear algebra and matrix to mean the factorization of a matrix into three matrices. Apart from linear algebra, singular value decomposition is also applied in data science. Understand this concept requires in-depth knowledge of Eigen decomposition. When computing SVD, you are trying to find the Eigenvalues and Eigenvectors of a matrix.
The linear transformation function works from one vector space to another vector space. This function takes into account the underlying linear structure of these vector spaces. It can also be called a map or linear operator. An endomorphism transformation occurs when the transformation's range is the same as the domain. On the other hand, if the range is invertible, then we have an automorphism transformation. The two vector spaces in linear transformation should have a similar underlying field.