Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Details about Norm of a vector and its problems
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
In this chapter we shall study the vector spaces over a field of reals or a field of complex numbers. For vector space over these fields we shall introduce an idea of the length of a vector and when the field is of real numbers, we shall also be able to introduce an idea of the angle between two vectors. After that we shall see that lengths and angles may be expressed interms of a certain type of scalar valued function which is called an inner product.
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Definitions and Problems on The matrix representation of a Linear transformation
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Discuss about T is unique, Direct sum, quotient space and its problems
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Definitions and problems on Invariant
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Explain about Projection
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Details about T linear, one-to-one and onto with problems
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Explain about Basis, N(T), R(T), Span dimension theorem of Linear transform
Problems of Linear
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Details about T is linear and its problems
Definition, Properties, Examples of Linear Transformation
Subject and UNIT: Random Process and Linear Algebra: Unit V: Linear Transformation and Inner Product Spaces,,
Details and examples about Linear Transformation
Subject and UNIT: Random Process and Linear Algebra: Unit IV: Vector Spaces,,
A basis β for a vector space V is a linearly independent subset of V that generates V. If β is a basis for V, we also say that the vectors of β form a basis for V. (or) A set S = {u1, u2, ..., un} of vectors is a basis of V if it has the following two properties. (1) S is linearly independent. (2) L(S) = V, i.e., every element of V is a linear combination of finite elements of S.
Subject and UNIT: Random Process and Linear Algebra: Unit IV: Vector Spaces,,
A subset S of a vector space that is not linearly dependent is called linearly independent. As before, we also say that the vectors of S are linearly independent. The following facts are true in any vector space. 1. The empty set is linearly independent, for linearly dependent sets must be non-empty. 2. A set consisting of a single non-zero vector is linearly independent. For if {u} is linearly dependent, then au = 0 for some non-zero scalar a.