Outrageously Funny Word Dictionary :: Orthogonal

👉 In mathematics, an orthogonality relationship is a mathematical concept that describes how two vectors can be orthogonal to each other. This means they are perpendicular or at right angles to each other in space. An orthogonality relationship between two vectors (u and v) states that their dot product (u . v) equals zero: \[ u \cdot v = 0 \] where \( u \) and \( v \) are the vectors. The term "orthogonal" refers to

orthogonally

👉 Orthogonalizing is a process used in mathematics and computer science to group or partition data into subsets that are similar but not identical. It is often used in fields such as signal processing, machine learning, and statistics to reduce the dimensionality of data while retaining important features. In the context of linear algebra, orthogonalizing groups elements means to transform them so that they can be represented as a basis (i.e., a set of vectors) for which the inner product between any two vectors is zero.

orthogonalizing

👉 In mathematics, an orthogonalized set is a subset of a vector space that contains all its non-zero vectors in the same direction. This means that it has the property that any two vectors in the set are orthogonal to each other. The term "orthogonalized" refers to the fact that these vectors have been transformed into a single, orthonormal basis.

orthogonalized

👉 The term "orthogonalize" in the context of mathematics refers to a transformation or mapping that changes the orientation or direction of vectors. This operation is often used in geometry and linear algebra, where it helps in transforming the coordinates of points on a two-dimensional plane into another coordinate system. In simpler terms, it's like taking a vector (a line segment) and turning it into an "axis" or a new set of axes that are perpendicular to each other. This transformation allows us to work

orthogonalize

👉 Orthogonalization is a mathematical concept in linear algebra and vector analysis. It refers to the process of aligning two vectors so that their directions are perpendicular, or orthogonal. This alignment results in two new vectors that are independent of each other, meaning they have no direct relationship with each other. In simpler terms: If you take two vectors (say A and B) and align them such that their direction is perpendicular to each other, then these two vectors will be orthogonal. In a more technical sense

orthogonalization

👉 Orthogonality is a mathematical concept in linear algebra. In this context, it refers to two vectors being orthogonal if their dot product (or inner product) equals zero. This means that the magnitude of the vector formed by these two vectors (the length or norm) must be equal for them to be considered orthogonal.

orthogonality

👉 In geometry and linear algebra, an orthogonal set of vectors (also known as a basis) is a subset of the vector space that spans it. In other words, two vectors in the same set are orthogonal if their dot product is zero. An orthogonal set can be thought of as a line or plane that contains all its vectors. This property is often used to describe geometric shapes and structures, such as planes, lines, or surfaces. Orthogonal sets have many important properties, including being closed under

orthogonal

👉 Orthogonality is a concept in geometry that refers to the property of two lines or planes being perpendicular to each other. When two lines are perpendicular, they form right angles (90°) at their point of intersection. The word "orthogonal" means opposite or perpendicular.

orthagoriscus

👉 Orthogonally aligned cladids are single-celled organisms that have a similar structure but do not share any genetic material. They are found in many different phyla of life, including bacteria, archaea, and eukaryotes.

Orthogonacladia

👉 Orthogonal is a system in which two or more objects are aligned parallel to each other, without any internal connections between them.

Orthogonalos