Gdtyjr

I am new to latex and I am trying to create this:

So far I have been able to create the matrices, like so:

[
 Ntextrm spectra
 beginbmatrix
 a_11 & a_12 & cdots & a_1M \
 a_21 & a_22 & cdots & a_2M \
 vdots & vdots & ddots & vdots \
 a_N1 & a_N2 & cdots & a_NM
 endbmatrix\
 quad
 beginbmatrix
 e_1 \
 e_2 \
 vdots \
 e_N
 endbmatrix
]

Does anyone know how can I add text above the matrices?

Try this with stackrel and mbox's

[
 Ntextrm spectra
 stackrelmbox$M$ components%
 beginbmatrix
 a_11 & a_12 & cdots & a_1M \
 a_21 & a_22 & cdots & a_2M \
 vdots & vdots & ddots & vdots \
 a_N1 & a_N2 & cdots & a_NM
 endbmatrix%
 quad
 stackrelstackrelmboxerrormboxdetection%
 beginbmatrix
 e_1 \
 e_2 \
 vdots \
 e_N
 endbmatrix%
 
]

The easiest way is to use array:

documentclassarticle
usepackageamsmath
begindocument
[
beginarrayccc
& & texterror \
& text$M$ components & textdetection \
text$N$ spectra &
beginbmatrix
 a_11 & a_12 & cdots & a_1M \
 a_21 & a_22 & cdots & a_2M \
 vdots & vdots & ddots & vdots \
 a_N1 & a_N2 & cdots & a_NM
endbmatrix &
beginbmatrix
 e_1 \
 e_2 \
 vdots \
 e_N
endbmatrix
endarray
]
enddocument

text where above the matrix? If you want a kind of heading above each column, then probably bordermatrix is your friend, a plain TeX command but usable in LaTeX.

If you want a single item over the whole matrix, then any latex stacking construct would do the job, stackrel or a second single column array environment with your bmatrix on the second row or....

update: sorry I see you want this second form, didn't notice the image link originally.

so....

[
 Ntextrm spectra
 beginsmallmatrix Mtextrm components\beginbmatrix
 a_11 & a_12 & cdots & a_1M \
 a_21 & a_22 & cdots & a_2M \
 vdots & vdots & ddots & vdots \
 a_N1 & a_N2 & cdots & a_NM
 endbmatrixendsmallmatrix quad
 beginsmallmatrix
 textrmerror\
 textrmdetection\
 beginbmatrix
 e_1 \
 e_2 \
 vdots \
 e_N
 endbmatrixendsmallmatrix
]

For future interest, if your labeling needs become more complicated, there is the qbordermatrix package which is somewhat more flexible than bordermatrix as you can label rows or columns and put the labels on any of the four sides of the matrix. I have used this a bit, but have just noticed that the delimiters seem to extend somewhat higher above the top row of matrix elements than I would like.

Some of the questions on the TikZ package have also been helpful for my early attempts at more complicated labeling of matrices. For example, see the responses on using braces to label some number of rows or columns of a matrix .

There is also the kbordermatrix package which seems initially designed to label the along the top and down the left side of a matrix. The documentation says
"I also have an experimental version that will put the labels on the right and bottom. If you ask, I will make it available."
This package does seem to do a better job than qbordermatrix of making the top of the delimiters an appropriate height above the top row of matrix elements.

For a more flexible solution I think I'm going to have to play with tikz more now that I know how to use tikz in amsmath environments like align and gather .