Why is the sum of outer products equal to the matrix product of a matrix and its transpose , so $A^TA = \sum_{i=1}^n a_i a_i^T$?
60598
Matrix $A^T A$ as sum of outer products
63803
Calculating the tensor product $\mathbb{Z}/n\mathbb{Z} \otimes_{\mathbb Z} \mathbb{Z}/n\mathbb{Z}$
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
143923
Why can the cross product of two vectors be calculated as the determinant of a matrix?
66709
Are the matrix products $AB$ and $BA$ similar?
57916
Transpose of product of matrices
15202
the root of $N$th transpose matrix
122202
How does the dot product convert a matrix into a scalar?
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
134989
Prove that if the identity is written as the product of $r$ transpositions, then $r$ is an even number
101040
Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
41514
Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
62030
$A^2=A^*A$. Why is matrix $A$ Hermitian?
25882
Is this algebraic identity obvious? $\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
109312
How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?