Related Experiment Video
Updated: May 22, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
New Kind of orthogonality in Normed spaces by using ϼ * -orthogonality
Laith Ahmed Jasim-ليث احمد جاسم محمد1, Mohammed Yahya Abed1
1University of Kerbala, Karbala, Karbala Governorate, Iraq.
Abstract:
Orthogonality is an important concept in normed spaces, and many generalizations of this concept have been proposed. In this paper, we introduce a new concept of orthogonality in normed spaces, denoted by -orthogonality, which is related to -orthogonality. The fundamental properties of this new concept are systematically analyzed, including symmetry, non-negativity, scalar homogeneity, linear independence of orthogonal vectors, the Cauchy-Schwarz type inequality, the zero property, and other characteristics. We also explain the relationship between this new definition and some other well-known types of orthogonality.
Related Concept Videos
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Orthogonal Trajectories
Scalar Product (Dot Product)
The scalar product of two vectors is obtained by multiplying...
Cartesian Vector Notation
Dot Product
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...