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What is linear algebra?
"Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another." (from Wikipedia)
What is an affine transformation?
An affine transformation is a linear transformation between vector spaces, followed by a translation.
What is the physical significance of null vectors?
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
Direction of vector in space is specified by?
It is an integral part of the vector and so is specified by the vector.
The components of a vector or what?
The components of a vector are magnitude and direction.
What is relationship between vector space and vector subspace?
Vector spaces can be formed of vector subspaces.
What has the author Tatsuo Kimura written?
Tatsuo Kimura has written: 'Introduction to prehomogeneous vector spaces' -- subject(s): Vector spaces
What has the author F Brickell written?
F. Brickell has written: 'Matrices and vector spaces' -- subject(s): Matrices, Problems, exercises, Vector spaces
What are practical applications of influence line diagrams?
What are the practical applications of influence line diagram
What are the engineering applications of vector calculus?
in which field vector calculus is applied deeply
What is the significance of orthonormality in the context of linear algebra and how does it relate to the concept of vector spaces?
Orthonormality is important in linear algebra because it simplifies calculations and makes it easier to work with vectors. In the context of vector spaces, orthonormal vectors form a basis that allows any vector in the space to be expressed as a linear combination of these vectors. This property is fundamental in many mathematical applications, such as solving systems of equations and understanding transformations in space.
What has the author Robert M Thrall written?
Robert M. Thrall has written: 'Vector spaces and matrices' -- subject(s): Vector spaces, Matrices 'A generalisation of numerical utilities 1'
What is the significance of the area vector in the context of vector calculus and its applications?
The area vector in vector calculus represents the direction and magnitude of a surface area. It is important in applications such as calculating flux, which measures the flow of a vector field through a surface. The area vector helps determine the orientation of the surface and is crucial for understanding the behavior of vector fields in three-dimensional space.
How would you define the zero vector 0?
The zero vector, denoted as 0, is a vector with all components equal to zero. It serves as the additive identity element in vector spaces, meaning that adding it to any vector does not change the vector's value.
What is linear algebra?
"Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another." (from Wikipedia)
What has the author Jean Schmets written?
Jean Schmets has written: 'Spaces of vector-valued continuous functions' -- subject(s): Continuous Functions, Locally convex spaces, Vector valued functions
Is computer applications a practical art?
no
