\noindent commands ignored

Question

Why are the \noindent commands ignored in the following code? The only indentation that I want is the paragraph preceding the two corollaries.

\documentclass[10pt]{amsart}
\usepackage{mathtools}
\begin{document}
We will review bilinear forms and the matrix representations for them. For a reference, one may refer to Applications of Linear Algebra by David C Lay, Judith McDonald, and Steven R Lay.
\vskip0.25in
\noindent \textbf{Corollary 1} \\vspace{1.25mm}
\noindent {\em $\mathcal{B}$ and $\mathcal{C}$ are two bases for $V$, and $P \in \mathrm{M}_{n}(F)$ is the transition matrix from $\mathcal{C}$ to $\mathcal{B}$. If $A$ is the matrix representation of a form on $V$ with respect to $\mathcal{B}$,}
\begin{equation}
A^{\prime} = P^{t}AP
\end{equation}
{\em is the matrix representation of the same form with respect to $\mathcal{C}$.} \
\vspace{0.25in}
\noindent \textbf{Corollary 2} \\vspace{1.25mm}
\noindent {\em If A is the matrix representation for a form on V with respect to a basis for $V$, for any invertible matrix $Q \in {\mathrm{M}}_{n}(F)$,}
\begin{equation}
A^{\prime} = Q A Q^{t}
\end{equation}
{\em is the matrix representation of the same form with respect to another basis for V.} \
\vspace{0.25in}
\end{document}

Answer 1

\noindent should almost never be used in a document, but if it is used it only does anything at the start of a paragraph.

so

\noindent\textbf{Corollary 1}

prevents the indentation of "Corollary" (this should be set with a theorem enviroment not a font change)

\noindent {\em $\mathcal{B}$ an

does nothing as it is mid-paragraph, the space before B is not a paragraph indent; it is a spurious word space added as you have a space (end of line) after \\\vspace{1.25mm}

I just added ths although I notice egreg added a similar example

\documentclass[10pt]{amsart}
\usepackage{mathtools}
\usepackage{amsthm}
\newtheoremstyle{break}%
{}{}%           % Note that final punctuation is omitted.
{\itshape}{}%
{\bfseries}{}%
{\newline}{}
\theoremstyle{break}
\newtheorem{cor}{Corollary}
\begin{document}
We will review bilinear forms and the matrix representations for
them. For a reference, one may refer to Applications of Linear Algebra
by David C Lay, Judith McDonald, and Steven R Lay.
\begin{cor}
  $\mathcal{B}$ and $\mathcal{C}$ are two bases for $V$, and
  $P \in \mathrm{M}_{n}(F)$ is the transition matrix from
  $\mathcal{C}$ to $\mathcal{B}$. If $A$ is the matrix representation
  of a form on $V$ with respect to $\mathcal{B}$,
\begin{equation}
A' = P^{t}AP
\end{equation}
is the matrix representation of the same form with respect to $\mathcal{C}$.
\end{cor}
\begin{cor}
  If A is the matrix representation for a form on V with respect to a
  basis for $V$, for any invertible matrix
  $Q \in {\mathrm{M}}_{n}(F)$,
\begin{equation}
A' = Q A Q^{t}
\end{equation}
is the matrix representation of the same form with respect to another
basis for V.
\end{cor}
\end{document}

Answer 2

Do you mean something like the following?

\documentclass[10pt]{amsart}
\usepackage{mathtools}
\newtheoremstyle{break}
 {0.25in}
 {0.25in}
 {\itshape}
 {0pt}
 {\bfseries\vspace{1.25mm}}
 {\newline}
 {0pt}
 {}
\theoremstyle{break}
\newtheorem{corollary}{Corollary}
\begin{document}
We will review bilinear forms and the matrix representations for them. 
For a reference, one may refer to Applications of Linear Algebra by 
David C.~Lay, Judith McDonald, and Steven R.~Lay.
\begin{corollary}
$\mathcal{B}$ and $\mathcal{C}$ are two bases for $V$, and 
$P \in \mathrm{M}_{n}(F)$ is the transition matrix from 
$\mathcal{C}$ to $\mathcal{B}$. If $A$ is the matrix 
representation of a form on $V$ with respect to $\mathcal{B}$,
\begin{equation}
A' = P^{t}AP
\end{equation}
is the matrix representation of the same form with respect to $\mathcal{C}$.
\end{corollary}
\begin{corollary}
If $A$ is the matrix representation for a form on $V$ with respect to 
a basis for $V$, for any invertible matrix $Q \in {\mathrm{M}}_{n}(F)$,
\begin{equation}
A' = Q A Q^{t}
\end{equation}
is the matrix representation of the same form with respect to another basis for $V$.
\end{corollary}
\end{document}