Newbetuts
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New posts in inner-products
Confused about a step in a proof that $a\times (b \times c) = (a\cdot c)b - (b\cdot c)a$
geometry
vector-spaces
vectors
proof-explanation
inner-products
What is a complex inner product space "really"?
intuition
inner-products
Proof: Sum of dimension of orthogonal complement and vector subspace
linear-algebra
vector-spaces
inner-products
Distance of a matrix from the orthogonal group
linear-algebra
matrices
metric-spaces
inner-products
Maximum angle between a vector $x$ and its linear transformation $A x$
optimization
eigenvalues-eigenvectors
inner-products
rotations
angle
Do orthonormal changes of basis affect the inner product?
linear-algebra
vector-spaces
inner-products
orthogonality
orthonormal
Proof of Cauchy-Schwarz inequality using a particular result from orthonormal sets
linear-algebra
inner-products
cauchy-schwarz-inequality
orthonormal
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
linear-algebra
functional-analysis
linear-transformations
inner-products
If every two-dimensional (vector) subspace of a normed space is an inner product space, then so is that normed space
functional-analysis
normed-spaces
inner-products
Inner product on $C(\mathbb R)$
linear-algebra
functional-analysis
inner-products
axiom-of-choice
A subspace $X$ is closed iff $X =( X^\perp)^\perp$
real-analysis
functional-analysis
hilbert-spaces
inner-products
Vector Algebra Coordinate Transformation
linear-algebra
vectors
inner-products
coordinate-systems
linear-transformations
What is "inner" about the inner product?
terminology
math-history
inner-products
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
functional-analysis
hilbert-spaces
inner-products
Dot product versus matrix multiplication, is the later a special case of the first?
matrices
inner-products
The Triangle Inequality implies that the shortest path between two points is a line segment. (in "Linear Algebra Done Right 3rd Edition" by Axler)
linear-algebra
inner-products
triangle-inequality
Is complex conjugation needed for valid inner product?
inner-products
Why is orthogonal basis important?
linear-algebra
vector-spaces
inner-products
orthogonality
Intuition for the Cauchy-Schwarz inequality
linear-algebra
inequality
inner-products
cauchy-schwarz-inequality
How do you prove that $tr(B^{T} A )$ is a inner product?
matrices
vector-spaces
inner-products
trace
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