I am a graduate student of Mathematics.I want to study dual spaces,linear functionals and transpose of a linear operator.But I am lacking a suitable text for that.I have tried Hoffmann Kunze and Friedberg-Insel-Spence but those books lack motivation.I am finding a book that gives motivation for studying dual spaces and also explains the theory nicely.Can someone help me find a suitable text?
2026-03-30 13:34:00.1774877640
Reference request for dual spaces.
99 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in DUAL-SPACES
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- How to conclude that $\ell_\infty$ is not separable from this exercise?
- Dual of linear map into a tensor product
- Basis of vector spaces in perfect pairing
- How to find a dual basis given a basis?
- $T \in \mathcal L(V,W)$ is surjective $\iff ($range $T)^0 = \{0\}$
- Restrict $g$ to a dense subclass in $\|f\|_p=\text{sup}\{|\int_Xfg|:\|g\|_{p'}\leq 1\}$
- $(\text{Im}(T^*))^0 = \ker(T)$?
- Unit ball in dual space is weak*separable
- Co- and contravariance of vectors vs co- and contravariant functors
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
There are two possibilities I can think of that you may wish to look at, and see if they suit your taste/learning style. One is Linear Algebra Done Right by Axler, which goes into all the topics you mention, although from memory doesn't go too deep into motivation. I do recall that the topic of dual spaces and functionals is dealt with pretty well. There are also lots of end-of-chapter problems, and solutions are pretty easily found online.
If you are affiliated with a university you can download it for free on the SpringerLink website: https://link.springer.com/book/10.1007/978-3-319-11080-6 (the material on dual spaces begins around p.101.)
Another one is Linear Algebra and Geometry by Kostrikin/Manin, which uses a geometric context to motivate most of the material covered, which is mostly upper-level linear algebra. They cover the topics you mentioned, but its been a while since I looked at it, so I can't recall the quality of the treatment of those topics specifically. However, the book is of very high quality, and I do remember getting a lot out of it. Anyway, take a look!