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What is an affine combination?
An affine combination is a linear combination of vectors in Euclidian space in which the coefficients add up to one.
Who discovered linear equations?
View all Sir William Rowan Hamilton invented the linear equation in 1843.
History of linear equation?
The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.
Example of linear functional in dual space?
dual space W* of W can naturally identified with linear functionals
What are some math topics?
Algebra, shape space and measure
What is an affine combination?
An affine combination is a linear combination of vectors in Euclidian space in which the coefficients add up to one.
What is an affine space?
An affine space is a vector space with no origin.
What is an affine group?
An affine group is the group of all affine transformations of a finite-dimensional vector space.
What is an affine variety?
An affine variety is a set of points in n-dimensional space which satisfy a set of equations which have a polynomial of n variables on one side and a zero on the other side.
What is unique basis?
A unique basis in linear algebra refers to a set of vectors that can uniquely express any vector in a vector space without redundancies or linear dependencies. This means that each vector in the space can be written as a unique linear combination of the basis vectors, making the basis choice essential for describing the space's dimension and properties.
Who discovered linear equations?
View all Sir William Rowan Hamilton invented the linear equation in 1843.
What is vector plane?
A vector plane is a two-dimensional space defined by a set of two non-parallel vectors. It represents all linear combinations of these vectors. In linear algebra, vector planes are used to visualize and understand relationships between vectors in space.
What is linear algebra used for?
Linear algebra is used to analyze systems of linear equations. Oftentimes, these systems of linear equations are very large, making up many, many equations and are many dimensions large. While students should never have to expect with anything larger than 5 dimensions (R5 space), in real life, you might be dealing with problems which have 20 dimensions to them (such as in economics, where there are many variables). Linear algebra answers many questions. Some of these questions are: How many free variables do I have in a system of equations? What are the solutions to a system of equations? If there are an infinite number of solutions, how many dimensions do the solutions span? What is the kernel space or null space of a system of equations (under what conditions can a non-trivial solution to the system be zero?) Linear algebra is also immensely valuable when continuing into more advanced math topics, as you reuse many of the basic principals, such as subspaces, basis, eigenvalues and not to mention a greatly increased ability to understand a system of equations.
What is an affine connection?
In the branch of mathematics called differential geometry, an affine connection is a geometrical object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.
History of linear equation?
The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.
What is the answer to page 3.15 in punchline algebra book A?
(space)A(space)Flip(space)Flop(space)
Why was cartesian coordinate system invented?
It allowed points in space to be described algebraically. This allowed lines and curves to be described using algebra. Bringing together algebra and geometry meant that tools that mathematicians had developed for solving algebraic problems could be applied to problems in geometry and tools from geometry could be applied to algebra.
